Question

find zeros of 2x^3-x^2-13x-6 using honors method fastly!!

Answer 1

Let p(x) = 2x³ − x² − 13x − 6

then, p(3) = 2 (3)³ − (3)²− 13 (3) − 6

⇒ p(3) = 2 × 27 − 9 − 39 − 6

⇒ p(3) = 54 − 54⇒ p(3) = 0

Since, p(3) is zero then, 3 is a zero of given Polynomial

As, p(3) = 0 Hence, (x − 3) is a factor of p(x)

Now ,we can write 2x³ − x² − 13x − 6 = 2x³ − 6x²+ 5x² − 15x + 2x − 6

= 2x² (x − 3) + 5x (x − 3) + 2 (x − 3)= (x − 3)

= (x − 3) (2x² + 5x + 2) = (x − 3)

{2x²+ 4x + x + 2} = (x − 3)

{2x (x + 2) + 1 (x + 2)} =(x − 3)

(x + 2) (2x + 1)

The value of (x − 3) (x + 2) (2x + 1) is zero.

when x − 3 = 0 or x + 2 = 0 or 2x + 1 = 0⇒ x = 3 or x = −2 or x = −12

Hence, all the zeroes of the polynomial are 3, −2 and −12.