Question

if -2 and 3 are the zeros of polynomial x²+(a+1)x+b then....find a,b​

Answer 1

Explanation:

Given,

P(x):

${x}^{2} + (a + 1)x + b$

We also know that -2 and 3 are the zeros of the polynomial.

=> when x = -2 or x = 3 the polynomial P(x) = 0

Now,

P(-2): 4 +2(a+1) + b = 0

=> 2a + b + 6 = 0 ----------1

Similarly,

P(3): 9 + 3(a+1) +b = 0

=> 3a + b + 12 = 0 --------2

Applying elemination method

subtracting equation 1 and 2,

3a + b + 12 = 0

2a + b + 6 = 0

(-) (-) (-)

_____________

a + 6 = 0

a = -6 ------- 3

Replacing the value of a from equation 3 to 1 we get,

b = -2a - 6

b = 12-6

b = 6

Thus,

a = -6

b = 6