Question

A quadratic polynomial whose zeros are 5 and -3, is
(a) +2x-15 (b) - 2x + 15 (c) - 2x-15 (d) none of these
​

Answer 1

Step-by-step explanation:

$Let \: \alpha \: and \: \beta \: be \: the \: zeroes$

Given

$\bull \: \: \: \alpha = 5 \\ \bull \: \: \: \beta = - 3$

$Sum \: o f \: zeroes = \alpha + \beta = 5 - 3 = 2$

$Product \: of \: its \: zeroes = \alpha \times \beta = 5 \times ( - 3) = - 15$

We know that,

${x}^{2} - ( \alpha + \beta )x + ( \alpha \times \beta )$

${x}^{2} - 2x - 15 = 0$

Verification

$Sum \: of \: its \: zeroes = \frac{ - b}{a} = - ( - 2) = 2$

$Product \: of \: its \: zeroes = \frac{c}{a} = \frac{ - 15}{1} = - 15$

Hence verified