165
Form a quadratic polynomial whose zeroes are twice the zeroes of polynomial $p(x) = x^2 - 3x - 5$.
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(b) Let $\alpha$ and $\beta$ be zeroes of $p(x)$
then $\alpha + \beta = 3$ and $\alpha\beta = -5$ (1)
Zeroes of required polynomial are $2\alpha$ and $2\beta$
$2\alpha + 2\beta = 6$ and $4\alpha\beta = -20$ (
frac{1}{2})
$\therefore$ Required polynomial is $x^2 - 6x - 20$ or $k(x^2 - 6x - 20)$ (
frac{1}{2})
(b) Let $\alpha$ and $\beta$ be zeroes of $p(x)$
then $\alpha + \beta = 3$ and $\alpha\beta = -5$ (1)
Zeroes of required polynomial are $2\alpha$ and $2\beta$
$2\alpha + 2\beta = 6$ and $4\alpha\beta = -20$ (
frac{1}{2})
$\therefore$ Required polynomial is $x^2 - 6x - 20$ or $k(x^2 - 6x - 20)$ (
frac{1}{2})