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Standard XIII

Mathematics

Relations between Roots and Coefficients : Higher Order Equations

If x2-3x+2 be...

Question

If $x^{2} - 3 x + 2$ be a factor of $x^{4} - p x^{2} + q$ , then (p, q) =

(3, 4)

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(4, 5)

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(4, 3)

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(5, 4)

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Solution

The correct option is D
(5, 4)

$x^{2} - 3 x + 2$ be factor of $x^{4} - p x^{2} + q = 0$

Hence $(x^{2} - 3 x + 2) = 0$ ⇒ (x-2)(x-1) = 0

⇒ x = 2, 1, putting these values in given equation

so, 4p - q -16 = 0 ......(i)

and, p - q - 1 = 0 .......(ii)

Solving (i) and (ii), we get (p, q) = (5, 4)

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If x2−3x+2 be a factor of x4−px2+q, then (p, q) =

The correct option is D (5, 4) x2−3x+2 be factor of x4−px2+q=0 Hence (x2−3x+2)=0 ⇒ (x-2)(x-1) = 0 ⇒ x = 2, 1, putting these values in given equation so, 4p - q -16 = 0 ......(i) and, p - q - 1 = 0 .......(ii) Solving (i) and (ii), we get (p, q) = (5, 4)

If $x^{2} - 3 x + 2$ be a factor of $x^{4} - p x^{2} + q$ , then (p, q) =