Question

Find the value of m so that 2x – 1 be a factor of 8x⁴ + 4x³ – 16x² + 10x + m.

Answer 1

Let p(x) = 8x⁴ + 4x³ – 16x² + 10x + m

Since, 2x – 1 is a factor of p(x), then put `p(1/2) = 0`

∴ `8(1/2)^4 + 4(1/2)^3 - 16(1/2)^2 + 10(1/2) + m = 0`

⇒ `8 xx 1/16 + 4 xx 1/8 - 16 xx 1/4 + 10(1/2) + m = 0`

⇒ `1/2 + 1/2 - 4 + 5 + m = 0`

⇒ 1 + 1 + m = 0

∴ m = –2

Hence, the value of m is –2.