Given the two quadratic equations: I. x 2 − 25 x + 156 = 0 x^2 - 25x + 156 = 0 x 2 − 25 x + 156 = 0 II. y 2 − 27 y + 182 = 0 y^2 - 27y + 182 = 0 y 2 −...

Question

Given the two quadratic equations:

I.

x225x+156=0x^2 - 25x + 156 = 0

II.

y227y+182=0y^2 - 27y + 182 = 0

If

xx
and
yy
are the roots of the respective equations, determine the correct relationship between
xx
and
yy
.

Options

A.
x<yx < y
B.
x>yx > y
C.
xyx \leq y
D.
x=y or no relation between x and yx = y \text{ or no relation between } x \text{ and } y
E.

<divclass="katexdisplay"><spanclass="katexdisplay"><spanclass="katex"><spanclass="katexmathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"display="block"><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></div><div class="katex-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><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></span></div>

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