Question

14. Given that 16x⁴+ - 4x³– 4b²x² + 7bx + 18 is divisible by 2x + b,

Answer 1

Answer:

(a) check the explanation

(b) the possible values of b is 6i or -29

Explanation:

Given function;

16x⁴ - 4x³– 4b²x² + 7bx + 18

(a)

factor of the given function = 2x + b

then, 2x + b = 0

x = -b/2

substitute the value of b into the given function;

16x⁴ - 4x³– 4b²x² + 7bx + 18

$16(\frac{-b}{2} )^4 -4(\frac{-b}{2})^3-4b^2(\frac{-b}{2})^2 +7b(\frac{-b}{2})+18=0\\\\b^4+\frac{b^3}{2} -b^4-\frac{7b^2}{2} +18=0\\\\\frac{b^3}{2} -\frac{7b^2}{2} +18=0\\\\multiply\ through \ by \ "2"\\\\b^3-7b^2+36 =0 \ (shown)$

(b)

b³ - 7b² + 36 = 0

b²(b - 7) + 36 = 0

b²(b - 7) = -36

b² = -36                or b - 7 = -36

b = √(-36)             or  b = -36 + 7

b = √(-1) x √(36)   or  b = -29

b = 6i       or   -29