Question

Find zeros of polnomial 6x^2-x-12and verify relationship between zeros and the coefficients.

Answer 1

Answer:-

Given Polynomial : 6x² - x - 12

By splitting the middle term,

→ 6x² - 9x + 8x - 12 = 0

→ 3x(2x - 3) + 4 (2x - 3) = 0

→ (3x + 4)(2x - 3) = 0

→ 3x + 4 = 0

→ 3x = - 4.

→ x = - 4/3

→ 2x - 3 = 0

→ 2x = 3

→ x = 3/2

Verification:

Let a = 6 ; b = - 1 , c = - 12.

Sum of the zeroes = - b/a

→ - 4/3 + 3/2 = - (- 1) / 6

→ (- 8 + 9) / 6 = 1/6

→ 1/6 = 1/6

Product of the zeroes = c/a

→ (- 4/3) * (3/2) = - 12 / 6

→ - 12/6 = - 12/6

Hence, Verified.