Question

Find the zeros of the following quadratic polynomial and verify the relation between the zeros and the coefficient x square - 15

Answer 1

Given :

• The quadratic equation = x² - 15

To Find :

• Find the zeros of the following quadratic polynomial and verify the relation between the zeros and the coefficient x² - 15.

Step-by-step explanation:

Let p(x) = x² - 15

Putting p(x) = 0

➨ x² - 15 = 0

➨ (x)² - (√15)² = 0

➨ (x - √15)(x + √15) = 0 {by using a² - b² = (a-b) (a+b)}

➨ x = √15 or - √15

Therefore, √15 and -√15 are the zeros of the polynomial.

Comparing with,

ax² + bx + c

a = 1 , b = 0 , c = -15

Verification :

Sum of zeroes = $\sf - \dfrac{Coefficient\:of\:x}{Coefficient\:of \:x^2}$

α + β = $\sf - \dfrac{-b}{a}$

L.H.S

=> α + β

=> √15 - √15

=> 0

R.H.S

=> - b/a

=> - 0/1

=> 0

L.H.S = R.H.S

Product of zeroes = $\sf - \dfrac{Constant\:term}{Coefficient\:of \:x^2}$

α × β = $\sf \dfrac{c}{a}$

L.H.S

=> α × β

=> (√15)(- √15)

=> - (√15)²

=> -15

R.H.S

=> c/a

=> -15/1

=> -15

L.H.S = R.H.S

Hence, relationship between zeroes and coefficient verified.