Given the two quadratic equations: (I) < s p a n c l a s s = " k a t e x " > < s p a n c l a s s = " k a t e x − m a t h m l &...

Question

Given the two quadratic equations:

(I) <spanclass="katex"><spanclass="katexmathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>x</mi><mo></mo><mn>56</mn><mo>=</mo><mn>0</mn></mrow><annotationencoding="application/xtex">x2+x56=0</annotation></semantics></math></span><spanclass="katexhtml"ariahidden="true"><spanclass="base"><spanclass="strut"style="height:0.8974em;verticalalign:0.0833em;"></span><spanclass="mord"><spanclass="mordmathnormal">x</span><spanclass="msupsub"><spanclass="vlistt"><spanclass="vlistr"><spanclass="vlist"style="height:0.8141em;"><spanstyle="top:3.063em;marginright:0.05em;"><spanclass="pstrut"style="height:2.7em;"></span><spanclass="sizingresetsize6size3mtight"><spanclass="mordmtight">2</span></span></span></span></span></span></span></span><spanclass="mspace"style="marginright:0.2222em;"></span><spanclass="mbin">+</span><spanclass="mspace"style="marginright:0.2222em;"></span></span><spanclass="base"><spanclass="strut"style="height:0.6667em;verticalalign:0.0833em;"></span><spanclass="mordmathnormal">x</span><spanclass="mspace"style="marginright:0.2222em;"></span><spanclass="mbin"></span><spanclass="mspace"style="marginright:0.2222em;"></span></span><spanclass="base"><spanclass="strut"style="height:0.6444em;"></span><spanclass="mord">56</span><spanclass="mspace"style="marginright:0.2778em;"></span><spanclass="mrel">=</span><spanclass="mspace"style="marginright:0.2778em;"></span></span><spanclass="base"><spanclass="strut"style="height:0.6444em;"></span><spanclass="mord">0</span></span></span></span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>x</mi><mo>−</mo><mn>56</mn><mo>=</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">x^2 + x - 56 = 0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8974em;vertical-align:-0.0833em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord mathnormal">x</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">56</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">0</span></span></span></span>

(II) <spanclass="katex"><spanclass="katexmathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>y</mi><mn>2</mn></msup><mo>+</mo><mn>17</mn><mi>y</mi><mo>+</mo><mn>72</mn><mo>=</mo><mn>0</mn></mrow><annotationencoding="application/xtex">y2+17y+72=0</annotation></semantics></math></span><spanclass="katexhtml"ariahidden="true"><spanclass="base"><spanclass="strut"style="height:1.0085em;verticalalign:0.1944em;"></span><spanclass="mord"><spanclass="mordmathnormal"style="marginright:0.03588em;">y</span><spanclass="msupsub"><spanclass="vlistt"><spanclass="vlistr"><spanclass="vlist"style="height:0.8141em;"><spanstyle="top:3.063em;marginright:0.05em;"><spanclass="pstrut"style="height:2.7em;"></span><spanclass="sizingresetsize6size3mtight"><spanclass="mordmtight">2</span></span></span></span></span></span></span></span><spanclass="mspace"style="marginright:0.2222em;"></span><spanclass="mbin">+</span><spanclass="mspace"style="marginright:0.2222em;"></span></span><spanclass="base"><spanclass="strut"style="height:0.8389em;verticalalign:0.1944em;"></span><spanclass="mord">17</span><spanclass="mordmathnormal"style="marginright:0.03588em;">y</span><spanclass="mspace"style="marginright:0.2222em;"></span><spanclass="mbin">+</span><spanclass="mspace"style="marginright:0.2222em;"></span></span><spanclass="base"><spanclass="strut"style="height:0.6444em;"></span><spanclass="mord">72</span><spanclass="mspace"style="marginright:0.2778em;"></span><spanclass="mrel">=</span><spanclass="mspace"style="marginright:0.2778em;"></span></span><spanclass="base"><spanclass="strut"style="height:0.6444em;"></span><spanclass="mord">0</span></span></span></span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>y</mi><mn>2</mn></msup><mo>+</mo><mn>17</mn><mi>y</mi><mo>+</mo><mn>72</mn><mo>=</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">y^2 + 17y + 72 = 0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.0085em;vertical-align:-0.1944em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">17</span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">72</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">0</span></span></span></span>

Find the correct relation between xx and yy based on the roots of these equations.

Options

A.

x<yx < y

B.

x>yx > y

C.

<spanclass="katex"><spanclass="katexmathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi><mo></mo><mi>y</mi></mrow><annotationencoding="application/xtex">xy</annotation></semantics></math></span><spanclass="katexhtml"ariahidden="true"><spanclass="base"><spanclass="strut"style="height:0.7719em;verticalalign:0.136em;"></span><spanclass="mordmathnormal">x</span><spanclass="mspace"style="marginright:0.2778em;"></span><spanclass="mrel"></span><spanclass="mspace"style="marginright:0.2778em;"></span></span><spanclass="base"><spanclass="strut"style="height:0.625em;verticalalign:0.1944em;"></span><spanclass="mordmathnormal"style="marginright:0.03588em;">y</span></span></span></span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi><mo>≤</mo><mi>y</mi></mrow><annotation encoding="application/x-tex">x \leq y</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7719em;vertical-align:-0.136em;"></span><span class="mord mathnormal">x</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span></span></span></span>

D.

x=yx = y or no relation between xx & yy

E.

<spanclass="katex"><spanclass="katexmathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi><mo></mo><mi>y</mi></mrow><annotationencoding="application/xtex">xy</annotation></semantics></math></span><spanclass="katexhtml"ariahidden="true"><spanclass="base"><spanclass="strut"style="height:0.7719em;verticalalign:0.136em;"></span><spanclass="mordmathnormal">x</span><spanclass="mspace"style="marginright:0.2778em;"></span><spanclass="mrel"></span><spanclass="mspace"style="marginright:0.2778em;"></span></span><spanclass="base"><spanclass="strut"style="height:0.625em;verticalalign:0.1944em;"></span><spanclass="mordmathnormal"style="marginright:0.03588em;">y</span></span></span></span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi><mo>≥</mo><mi>y</mi></mrow><annotation encoding="application/x-tex">x \geq y</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7719em;vertical-align:-0.136em;"></span><span class="mord mathnormal">x</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≥</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span></span></span></span>

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