Question

zeros of the polynomial X^2 + (a+ 1)x+b are 2 and- 3 ,then find the value of a + b

Answer 1

Hey there!

Given polynomial f(x) = x² + ( a + 1 ) x + b

Also, 2 & -3 are the zeroes of the polynomial.

According to factor theorem , If a is a zero of the polynomial of f(x) , then f(a) = 0

2 is a zero of the polynomial x² + ( a + 1 ) x + b ,

Now, f(2) = 0
2² + ( a + 1 )2 + b = 0
6 +2 a + b = 0
2a + b = -6 ...Equation(1)

-3 is a zero of the polynomial x² + ( a + 1 ) x + b ,

Now, f(-3) = 0
(-3)² + ( a + 1 )-3 + b = 0
9- 3 -3 a + b = 0
6 - 3a + b = 0
3a - b = 6 ...Equation(2)

Now, Solving equation(1) & (2)

3a - b = 6
2a + b = -6
==========
5a = 0
a = 0

Now , 2a + b = -6
2(0) + b = -6
b = -6

Therefore, a + b = 0-6 = -6 .

Hope helped!