Question

If '2' is the zero of both the polynomials 3x² +mx -14 and 2x³ + nx² + x - 2, then the value of m - 2n is

Answer 1

2 is zero of polynomial 3x² + mx - 14

3 x 2² + 2m - 14 = 0

⇒ 2m = 14 - 12 = 2

⇒ m = 1

Also, 2 is zero of polynomial 2x³ + nx² + x - 2

\(\therefore\) 16 + 4n + 2 - 2 = 0

⇒ 4n = 16

⇒ n = -4

\(\therefore\) m - 2n = 1 + 8 = 9