Question

a quadratic polynomial has sum of zeros 2 and product of zeroes are - 3/7. find the polynomial ​

Answer 1

$\sf\huge\bold{Answer:}$

Given :

In a polynomial,

Sum of zeroes = $2$

Product of zeroes = $\frac{ - 3}{7}$

To Find :

Quadratic polynomial.

Solution :

General form of a quadratic equation

$⇒ {x}^{2} - Sx + P = 0$

where S = sum of zeroes

and P = product of zeroes.

Inserting values of S and P in the general polynomial,we get

$⇒ {x}^{2} - (2)x + (\frac{ - 3}{7}) = 0$

On removing bracket,we obtain

$⇒ {x}^{2} - 2x - \frac{3}{7} = 0$

On simplifying,

$⇒7({x}^{2} - x - \frac{3}{7}) = 7(0)\\ ⇒7 {x}^{2} - 7x - 3 = 0$

Hence,a quadratic polynomial having sum of zeros 2 and product of zeroes are - 3/7 is

$⇒7 {x}^{2} - 7x - 3 = 0$