Question

Find a quadratic polynomial with 6 and -3 as the sum and product of its zeroes respectively.​

Answer 1

S O L U T I O N :

Let the zeroes of the polynomial be α & β respectively.

A/q

$\underline{\mathcal{SUM\:OF\:ZEROES\::}}$

$\mapsto\tt{\alpha + \beta = \dfrac{-b}{a} =\bigg\lgroup\dfrac{Coefficient\:of\:x}{Coefficient\:of\:x^{2}} \bigg\rgroup }$

$\mapsto\tt{\alpha + \beta = 6}$

$\underline{\mathcal{PRODUCT\:OF\:ZEROES\::}}$

$\mapsto\tt{\alpha \times \beta = \dfrac{c}{a} =\bigg\lgroup\dfrac{Constant\:term}{Coefficient\:of\:x^{2}} \bigg\rgroup }$

$\mapsto\tt{\alpha \times \beta = -3}$

Now,

As we know that required quadratic polynomial are :

→ x² - (sum of zeroes)x + (product of zeroes)

→ x² - (6)x + (-3)

→ x² - 6x - 3