If the zeroes of p x are double the zeroes of the polynomial q x - x 2-4 x -3- then p x isA- x2-8 x-12B- x2-4 x-3- 4 x2-4 x-8D- 2 x2-8 x-4

The correct option is A x^2 8x + 12Splitting the middle term of q(x), we have, x^2 4x+3 ⇒ x^2 x 3x + 3 ⇒ x(x 1) 3(x 1) ⇒ (x 3)(x 1) ∴The zeroes of ...

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Standard IX

Mathematics

Factor of Polynomials

If the zeroes...

Question

If the zeroes of p(x) are double the zeroes of the polynomial q(x) = $x^{2} - 4 x + 3$ , then p(x) is

x^{2} - 8 x + 12

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2 x^{2} - 8 x + 4

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x^{2} - 4 x + 3

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4 x^{2} - 4 x + 8

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Solution

The correct option is A $x^{2} - 8 x + 12$
Splitting the middle term of $q (x)$ , we have,
$x^{2} - 4 x + 3$
$\Rightarrow$ $x^{2} - x - 3 x + 3$
$\Rightarrow$ $x (x - 1) - 3 (x - 1)$
$\Rightarrow$ $(x - 3) (x - 1)$
$∴$ The zeroes of $q (x)$ are 1 and 3.
We know, zeroes of $p (x)$ are double that of q(x).
$\Rightarrow$ The zeroes of p(x) are 2 and 6.
$\Rightarrow p (x) = (x - 2) (x - 6)$
$\Rightarrow$ $p (x) = x^{2} - 8 x + 12$

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If the zeroes of p(x) are double the zeroes of the polynomial q(x) = x2−4x+3, then p(x) is

If the zeroes of p(x) are double the zeroes of the polynomial q(x) = $x^{2} - 4 x + 3$ , then p(x) is