Question

write a quadratic polynomial if sum and product of zeroes are -7 and 4

Answer 1

✒Question :

Write a quadratic polynomial if sum and product of zeroes are -7 and 4 ?

✒Answer :

$sum = \alpha + \beta = - 7$

$product = \alpha \beta = 4$

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

$k(x) = {x}^{2} - ( - 7)x + 4$

$k(x) = {x}^{2} + 7x + 4$

.: it is the required polynomial .

✨HOPE IT HELPS YOU :-)

Answer 2

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

FORMULA TO BE IMPLEMENTED

If the zeroes of the quadratic polynomial are given, then the quadratic polynomial is obtained as

${x}^{2} - ( \: sum \: of \: the \: zeros \: )x + product \: of \: the \: zeros \:$

GIVEN

A quadratic polynomial, whose zeroes are - 7 and 4

TO DETERMINE

The quadratic polynomial

EVALUATION

The Zeros are - 7 & 4

So

Sum of the zeroes

= - 7 + 4

= - 3

Product of the Zeros

= (- 7 ) × 4

= - 28

So the required polynomial is

${x}^{2} - ( \: sum \: of \: the \: zeros \: )x + product \: of \: the \: zeros \:$

$= {x}^{2} + 3x - 28$