Question

13. A Quadratic polynomial
whose sum and product of
zeros are -3 and 2 is

a) x^2-3x+2
b) x^2+3x+2
c) x^2+2x+3​

Answer 1

Given :

• A Quadratic polynomial whose sum and products of zeros are -3 and 2 .

To Find :

• The Quadratic equation formed from given roots =?

Formula :

(1) Formula Method :

$\\ \bullet \sf \: x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac} }{2a}$

(2) Determinant Method :

$\bullet \sf \: D = {b}^{2} - 4ac$

(3) Sum of the roots :

$\implies \sf \: sum \: of \: the \: roots \: = \alpha + \beta$

(4) Product of the roots

$\implies \sf \: product \: of \: the \: roots = \alpha \beta$

(5) Formation of Quadratic equation :

$\implies \sf \: {x}^{2} - ( \alpha + \beta )x + \alpha \beta = 0$

Solution :

A Quadratic polynomial whose

$\bullet \sf \: sum = \alpha + \beta = - 3$

$\\ \bullet \sf \: product = \alpha \beta = 2$

By using formation of quadratic equation :

$\implies \sf \: {x}^{2} - ( \alpha + \beta )x + \alpha \beta = 0 \\ \\ \\ \implies \sf \: \underline{ \red{ \bf{substituting \: given \: values :}} } \\ \\ \implies \sf \: {x}^{2} - ( - 3)x + 2 = 0 \\ \\ \\ \implies \sf \: {x}^{2} + 3x + 2 = 0 \\ \\ \\ \implies \boxed{ \sf{ {x}^{2} + 3x + 2 = 0}}$

The Quadratic equation will be,

=> x²+3x+2=0