Question

If4and-2 are the zeros of the quadratic polynomial then find the quadratic polynomial

Answer 1

Given :-

• 4 , -2 are the zeros of Quadratic polynomial

To find :-

• Quadratic polynomial

Solution :-

If ${\alpha, \beta}$ are the zeros of Quadratic polynomial then required Quadratic polynomial is

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

Here ,

$\alpha = 4 \\ \beta = - 2$

$\alpha + \beta = 4 + ( - 2)$

$\alpha + \beta = 4 - 2$

$\alpha + \beta = 2$ __ eq 1

$\alpha \beta = (4)( - 2)$

$\alpha \beta = - 8$ __ eq 2

Substituting the values

Required Quadratic polynomial is ,

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

$x {}^{2} - ( 2)x + ( - 8)$

$x {}^{2} - 2x - 8$

So, the required Quadratic polynomial is x² - 2x -8