Question

show that P (x) = x² + 3x²+2x-6 has a
realzero.​

Answer 1

Answer:

Given polynomial : p(x) = x² + 3x² + 2x - 6

→ p(x) = 4x² + 2x - 6

Using Middle Term Factorisation.

→ p(x) = 4x² + 6x - 4x - 6

→ p(x) = 2x(2x + 3) - 2(2x + 3)

→ p(x) = (2x - 2)(2x + 3)

To find the zeroes, these factors should be equal to zero.

Using Zero Product Rule.

→ (2x - 2) = 0 or (2x + 3) = 0

→ x = 2/2 or x = - 3/2

→ x = 1 or - 3/2

Hence, the above polynomial has real zeroes.