Question

Find the quadratic polynomial, sum, and product of whose zeroes are −1 and −20 respectively. Also, find the zeroes of the polynomial so obtained.

Answer 1

We have been given the sum of zeroes and product of zeroes
Let us consider the general polynomial

`p(x) = ax^2 + bx + c`

Sum of zeroes is `(-b)/a`

And product of zeroes is `c/a`

According to question

`(-b)/a = -1  "and"  c/a = -20`

Assuming a = 1

-b = -1

⇒ b = 1

And c = -20

So, the polynomial so formed is `p(x) = x^2 + x - 20`

To find the zeroes of the polynomial equate polynomial to zero.

`x^2 + x - 20 = 0`

`x^2 + 5x - 4x - 20 = 0`

`x(x + 5) - 4(x + 5) = 0`

(x + 5)(x - 4) = 0

⇒ x = -5,4

Therefore, zeroes of the polynomial are -5 and  4.