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(x±a)(x±b) = x²±(a+b)x+ab.

For which val...

Question

For which value of a and b, the zeroes of $q (x) = x^{3} + 2 x^{2} + a$ are also the zeroes of the polynomial $p (x) = x^{5} - x^{4} - 4 x^{3} + 3 x^{2} + 3 x + b$ ?

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Solution

$\Rightarrow 3 - a - 4 = 0, 3 a + 3 = 0, b - 2 a = 0$
$\Rightarrow - a - 1 = 0, 3 (a + 1) = 0, b = 2 a$
$\Rightarrow - a = 1, a = - 1, b = 2 a$
$∴ a = - 1$ , $b = 2 a = 2 \times - 1 = - 2$
$∴ a = - 1, b = - 2$
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