Question

if (x+2) and (x-2) are factors of p(x) =x^3+3x^2-2ax+b, find the values of a and b.

Answer 1

p(x) = x³ + 3 x² - 2 ax + b

x + 2 is a factor

By factor theorem p( - 2 ) = 0

==> (-2)³ + 3(-2)² - 2 a(-2) + b = 0

==> - 8 + 12 + 4 a + b = 0

==> 4 a + b + 4 = 0 ................................(1)

x - 2 is a factor.

By Factor Theorem p(2) = 0

==> (2)³ + 3(2)² - 2 a(2) + b = 0

==> 8 + 12 - 4 a + b = 0

==> b - 4 a + 20 = 0 ................................(2)

Adding (1) and (2) we get :

2 b + 24 = 0

==> 2 b = -24

==> b = -24/2

==> b = -12

b - 4 a + 20 = 0

==> - 12 - 4 a + 20 = 0

==> - 4 a = - 8

==> a = -8/-4

==> a = 2

The values are :

a = 2

b = -12

Hope it helps

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Answer 2

Given that x-2=0
X=2
Now putting x=2in p(x)

2^3+3×2^2-2a×2+b=0







Solve this and again putting x=-2in p(x) and solve u get a equation then equating both ration