Question

Polynomial , Find a quadratic polynomial whoes zero are given below : - 5, - 7​

Answer 1

Question

Find a quadratic polynomial whoes zero are given below : - 5, - 7 .

Answer = x²+12x+35

Step by step explanation

Given

• Zeros of polynomial f(x) are -5 and -7

To Find

• Quadratic polynomial whoes zero are given below : - 5, - 7.

Solution

$let \: \alpha = - 5 \: and \: \beta = - 7$

$\sf Sum \: of \: zeros ( \alpha + \beta )= -5+(-7)$

$\sf Sum \: of \: zeros ( \alpha + \beta )= -5-7$

$\sf Sum \: of \: zeros ( \alpha + \beta )= -12$

${\sf Product \: of \: zeros \: (\alpha \beta ) = - 5 \times ( -7 )}$

${\sf Product \: of \: zeros \: (\alpha \beta ) = - 5 \times -7 }$

${\sf Product \: of \: zeros \: (\alpha \beta ) = 35}$

$\mathfrak{f(x) = {x}^{2} - (Sum \: of \: zeros)x + Product \: of \: zeros}$

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

$\mathfrak{f(x) = {x}^{2} - ( - 12 )x + 35}$

$\mathfrak{f(x) = {x}^{2} + 12 x + 35}$

$~~~~~~\text{The Quadratic polynomial whoes zero}\\{\text{ are -5 and -7 is \pink{x²+12x+35}}}$