Question

if a-b=7,and x-2 is a factor of X3+ax2+bx+18 then find a and b​

Answer 1

The correct answer is a = -2 and b = -9.

Given: The equation = $x^{3}+ax^{2} +bx+18 = 0$.

a - b = 7.

To Find: Value of a and b.

Solution:

If (x-2) is a factor of $x^{3}+ax^{2} +bx+18 = 0$ the x=2 should satisfy the equation.

$2^{3} +a(2)^{2} +2b+18=0$

8 + 4a + 2b + 18 = 0

2a + b = -13

a-b = 7 (given)

a = b+7

Put in 2a + b = -13.

2(b+7) + b = -13

2b+14+b = -13

3b = -27

b = -9

a = b+7 = -9+7 = -2

Hence the value of a = -2 and b = -9.

#SPJ2