Question

Find the zeroes of the quadratic polynomial t2 -9 and verify the relationship
between the coefficients and its zeroes.

Answer 1

Answer:

Zeros are 3 & -3

Explanation:

Given polynomial,

⇒ t² - 9

Or, it can be written as,

⇒ (t)² - (3)²

Using the identity :- a² - b² = (a + b)(a - b)

We can say that,

⇒ (t)² - (3)² = (t + 3)(t - 3)

Then, zeros of the polynomial are

⇒ t = 3, -3

Verification of the relationship between the coefficient and it's zeros,

Sum of zeros,

• α + β = 3 + (-3) = 0

Product of zeros,

• αβ = (3)(-3) = -9

Hence, verified !

_____________________

General form of a quadratic equation :-

• ax² + bx + c

Identity used :-

• (a + b)(a - b) = a² - b²