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="katex−mathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>11</mn><mi>x</mi><mo>+</mo><mn>28</mn><mo>=</mo><mn>0</mn></mrow><annotationencoding="application/x−tex">x2−11x+28=0</annotation></semantics></math></span><spanclass="katex−html"aria−hidden="true"><spanclass="base"><spanclass="strut"style="height:0.8974em;vertical−align:−0.0833em;"></span><spanclass="mord"><spanclass="mordmathnormal">x</span><spanclass="msupsub"><spanclass="vlist−t"><spanclass="vlist−r"><spanclass="vlist"style="height:0.8141em;"><spanstyle="top:−3.063em;margin−right:0.05em;"><spanclass="pstrut"style="height:2.7em;"></span><spanclass="sizingreset−size6size3mtight"><spanclass="mordmtight">2</span></span></span></span></span></span></span></span><spanclass="mspace"style="margin−right:0.2222em;"></span><spanclass="mbin">−</span><spanclass="mspace"style="margin−right:0.2222em;"></span></span><spanclass="base"><spanclass="strut"style="height:0.7278em;vertical−align:−0.0833em;"></span><spanclass="mord">11</span><spanclass="mordmathnormal">x</span><spanclass="mspace"style="margin−right:0.2222em;"></span><spanclass="mbin">+</span><spanclass="mspace"style="margin−right:0.2222em;"></span></span><spanclass="base"><spanclass="strut"style="height:0.6444em;"></span><spanclass="mord">28</span><spanclass="mspace"style="margin−right:0.2778em;"></span><spanclass="mrel">=</span><spanclass="mspace"style="margin−right:0.2778em;"></span></span><spanclass="base"><spanclass="strut"style="height:0.6444em;"></span><spanclass="mord">0</span></span></span></span>
(II) <spanclass="katex"><spanclass="katex−mathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>y</mi><mn>2</mn></msup><mo>+</mo><mn>13</mn><mi>y</mi><mo>+</mo><mn>30</mn><mo>=</mo><mn>0</mn></mrow><annotationencoding="application/x−tex">y2+13y+30=0</annotation></semantics></math></span><spanclass="katex−html"aria−hidden="true"><spanclass="base"><spanclass="strut"style="height:1.0085em;vertical−align:−0.1944em;"></span><spanclass="mord"><spanclass="mordmathnormal"style="margin−right:0.03588em;">y</span><spanclass="msupsub"><spanclass="vlist−t"><spanclass="vlist−r"><spanclass="vlist"style="height:0.8141em;"><spanstyle="top:−3.063em;margin−right:0.05em;"><spanclass="pstrut"style="height:2.7em;"></span><spanclass="sizingreset−size6size3mtight"><spanclass="mordmtight">2</span></span></span></span></span></span></span></span><spanclass="mspace"style="margin−right:0.2222em;"></span><spanclass="mbin">+</span><spanclass="mspace"style="margin−right:0.2222em;"></span></span><spanclass="base"><spanclass="strut"style="height:0.8389em;vertical−align:−0.1944em;"></span><spanclass="mord">13</span><spanclass="mordmathnormal"style="margin−right:0.03588em;">y</span><spanclass="mspace"style="margin−right:0.2222em;"></span><spanclass="mbin">+</span><spanclass="mspace"style="margin−right:0.2222em;"></span></span><spanclass="base"><spanclass="strut"style="height:0.6444em;"></span><spanclass="mord">30</span><spanclass="mspace"style="margin−right:0.2778em;"></span><spanclass="mrel">=</span><spanclass="mspace"style="margin−right:0.2778em;"></span></span><spanclass="base"><spanclass="strut"style="height:0.6444em;"></span><spanclass="mord">0</span></span></span></span>
Find the correct relationship between x and y from the options below.
Options
If x>y
If <spanclass="katex"><spanclass="katex−mathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi><mo>≥</mo><mi>y</mi></mrow><annotationencoding="application/x−tex">x≥y</annotation></semantics></math></span><spanclass="katex−html"aria−hidden="true"><spanclass="base"><spanclass="strut"style="height:0.7719em;vertical−align:−0.136em;"></span><spanclass="mordmathnormal">x</span><spanclass="mspace"style="margin−right:0.2778em;"></span><spanclass="mrel">≥</span><spanclass="mspace"style="margin−right:0.2778em;"></span></span><spanclass="base"><spanclass="strut"style="height:0.625em;vertical−align:−0.1944em;"></span><spanclass="mordmathnormal"style="margin−right:0.03588em;">y</span></span></span></span>
If x<y
If <spanclass="katex"><spanclass="katex−mathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi><mo>≤</mo><mi>y</mi></mrow><annotationencoding="application/x−tex">x≤y</annotation></semantics></math></span><spanclass="katex−html"aria−hidden="true"><spanclass="base"><spanclass="strut"style="height:0.7719em;vertical−align:−0.136em;"></span><spanclass="mordmathnormal">x</span><spanclass="mspace"style="margin−right:0.2778em;"></span><spanclass="mrel">≤</span><spanclass="mspace"style="margin−right:0.2778em;"></span></span><spanclass="base"><spanclass="strut"style="height:0.625em;vertical−align:−0.1944em;"></span><spanclass="mordmathnormal"style="margin−right:0.03588em;">y</span></span></span></span>
If x=y or no relation can be established between x and y