Find the zeroes of the quadratic polynomial p(x) = 6x² – 3 – 7x. And also, verify the relationship between zeroes and coefficient.

To Find: Zeroes of the polynomial

Given: p(x) = 6x² – 3 – 7x

Concept Used:

For a quadratic polynomial,

P(x) = ax² + bx + c

Sum of the roots

The product of roots

Explanation:

P(x) = 0

6x² – 3 – 7x = 0

6x² – 7x – 3 = 0

(We factorized 7 such that the product is equal to 18 and the difference is equal to 7)
6x² + 2x – 9x – 3 = 0
2x(3x + 1) – 3(3x + 1) = 0

(3x + 1)(2x – 3) = 0

Now, to verify the relationship,

Sum of the zeroes

The product of the zeroes

Hence, verified.