Question

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

Answer 1

Solution :

The given polynomial is

f(x) = x² + (a + 1)x + b

Since 2 and - 3 are zeroes of f(x),

f(2) = 0

or, 2² + (a + 1) (2) + b = 0

or, 4 + 2a + 2 + b = 0

or, 2a + b + 6 = 0 ... (i)

and f(- 3) = 0

or, (- 3)² + (a + 1) (- 3) + b = 0

or, 9 - 3a - 3 + b = 0

or, 3a - b - 6 = 0 ... (ii)

Adding (i) and (ii), we get

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

or, 5a = 0

or, a = 0

From (i), we get

2 (0) + b + 6 = 0

or, b = - 6

Hence, the required polynomial is

f(x) = x² + x - 6 .