Question

if 2 is the zero of the both of the polynomial 3x2+mx - 14 and 2x3 + nx2+ X - 2 then the value of m- 2n is​

Answer 1

Question :–

▪︎ If 2 is the zero of the both of the polynomial 3x² + mx - 14 = 0 and 2x³ + nx²+ x - 2 = 0 then the value of m- 2n = ?

ANSWER :–

▪︎ m - 2n = 9

EXPLANATION :–

GIVEN :–

▪︎ 2 is the zero of the both of the polynomial 3x² + mx - 14 = 0 and 2x³ + nx² + x - 2 = 0.

TO FIND :–

Value of (m - 2n)

SOLUTION :–

⮕ Every root of polynomial will always satisfy the polynomial.

☞ Applying in first equation –

⇒ 3(2)² + m(2) - 14 = 0

⇒ 3(4) + 2m - 14 = 0

⇒ 2m = 14 - 12

⇒ m = 1

☞ Now Applying in second equation –

⇒ 2(2)³ + n(2)² + 2 - 2 = 0

⇒ 16 + 4n = 0

⇒ n = -4

☞ Now –

⇒ m - 2n = 1 - 2(-4)

⇒ m - 2n = 9