Question

find the values of a and b, so the (x-1)and (x+2) are factor of x^3 + 10x^2+ax+b

Answer 1

Step-by-step explanation:

Let,

=> x-1 = 0

=> x = 1

Similarly,

=> x = 2

Now, We will put these both value of x in two equations :-.

=> P(x) = x^3-10x^2+ax+b

=> P(1) = (1)^3 -10(1)^2+a x 1 + b

=> 0 = 1 - 10 + a+b

=> 0 = -9 + a + b --------- (1)

Again,

=>P(2) = (2)^3 - 10(2)^2 + 2a +b

=> 0 = 8 - 40 + 2a + b

=> 0 = -32 + 2a +b ---------- (2)

Eq (1) - (2)

-9 + a + b = 0

-(-32 + 2a + b) = 0

________________

-23 + a = 0

=> a = 23

Putting value of 'a' in equation 2.

=> 0 = -32 + 2 x 23 + b

=> -b = -32+46

=> -b = 14

=> b = -14

Again,

Putting value of 'a' in equation 1.

=> 0 = -9 + a + b

=> 0 = -9 + 23 + b

=> -b = 14

=> b = -14