Question

If 2 and -2are the zeroes of the polynomial
P(x)=ax⁴+2x³-3x²bx-4, find the value of and b.

Answer 1

p(x) = ax⁴ + 2x³ - 3x² + bx - 4

Two of the four zeroes = 2 and -2

put x = 2, So p(2) = 0

==> a(2)⁴ + 2(2)³ - 3(2)² + 2(b) - 4 = 0

==> 16a + 16 - 12 + 2b - 4 = 0

==> 16a + 2b = 0

==> 8a + b = 0 ...(1)

put x = -2, So p(-2) = 0

==> a(-2)⁴ + 2(-2)³ - 3(-2)² + b(-2) - 4 = 0

==> 16a - 16 - 12 - 2b - 4 = 0

==> 16a - 2b = 32

==> 8a - b = 16 ...(2)

Add (1) and (2):

==> 8a + b + 8a - b = 16 + 0

==> 16a = 16

==> a = 1

Putting value of a in eq(1)

==> 8a + b = 0

==> b = -8a

==> b = -8

Hence, value of a is 1 and b is -8