Express r in terms of p and q if the roots of the equation x 2- px - q -0 are - - and the roots of the equation x 2- rx - s -0 are -4- -4A-B- -C- -p-2 q-a-2 qD- 2 q- p-2 q

The correct option is A α + β = p, αβ = q α^4 + β^4 = r ex = (α^2 + β^2)^2 2α^2β^2 ex = ((α+ β)^2 2αβ)^2 2α^2β^2 r = (p^2 2q)^2 2q^2 ...

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Quantitative Aptitude

Maxima/Minima of a Quadratic Equation

Express r in ...

Question

Express r in terms of p and q if the roots of the equation $x^{2} + p x + q = 0$ are $α, β$ and the roots of the equation
$x^{2} - r x + s = 0$ are $α^{4}, β^{4}$

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p - 2q - 2q

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2q - p - 2q

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Solution

The correct option is A
-

$α + β$ = -p, $α β$ = q
$α^{4} + β^{4}$ = r
= $(α^{2} + β^{2})^{2}$ - 2 $α^{2} β^{2}$
= $((α + β)^{2} - 2 α β)^{2} - 2 α^{2} β^{2}$
r = $(p^{2} - 2 q)^{2} - 2 q^{2}$

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Express r in terms of p and q if the roots of the equation x2+px+q=0 are α,β and the roots of the equation x2−rx+s=0 are α4,β4

The correct option is A - α+β = -p, αβ = q α4+β4 = r = (α2+β2)2 - 2α2β2 = ((α+β)2−2αβ)2−2α2β2 r = (p2−2q)2−2q2

Express r in terms of p and q if the roots of the equation $x^{2} + p x + q = 0$ are $α, β$ and the roots of the equation
$x^{2} - r x + s = 0$ are $α^{4}, β^{4}$

The correct option is A
-

$α + β$ = -p, $α β$ = q
$α^{4} + β^{4}$ = r
= $(α^{2} + β^{2})^{2}$ - 2 $α^{2} β^{2}$
= $((α + β)^{2} - 2 α β)^{2} - 2 α^{2} β^{2}$
r = $(p^{2} - 2 q)^{2} - 2 q^{2}$