Question

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

Answer 1

Step-by-step explanation:

Given quadratic polynomial is

x²+(a+1)x+b

Also given,

zeros are 2,-3

Now consider,

x² + (a+1)x + b

= (2)² + (a+1)(2) + b

= 4+2a+2+b

= 2a+b+6 = 0

2a+b = -6----------- (1)

Now consider,

x² + (a+1)x + b

= (-3)² + (a+1)(3) + b

= 9+3a+3+b

= 3a+b+12=0

3a+b = -12--------- (2)

By solving equation (1)&(2)

(1)×(1) = 2a+b = -6

(2)×(1) = 3a+b = -12

(-) (-) (+)

_______________

-a = 6

:. a = -6

Substitute 'a' value in equation (1)

=> 2a+b = -6

=> 2(-6)+b= -6

=> -12 + b = -6

=> b = -6 + 12

:. b = 6.

:. a=-6,b=6