Question

4. If –2 and 3 are the zeroes of the polynomial P(x) 2x3 – x2 + ax + b then find the values
of a and b.​

Answer 1

Step-by-step explanation:

Given:

1. p(x)=2x³-x²+ ax + b.
2. x=-2 and x=3.

To find: values of a and b.

If x=-2 then,

p(-2)=2×(-2)³-(-2)²+a(-2)+b

=> 2×(-8)-(4)-2a+b

=> -16-4-2a+b

=> b-2a=20-----(1(

If x=3 then,

p(3)=2×(-3)³-(3)²+a(3)+b

=> 2×(-27)-9+3a+b

=> -54-9+3a+b

=> -63+3a+b=0

=> 3a+b=63------(2).

By (2)-(1):

=> 3a+b-(b-2a)=63-20

=> 3a+b-b+2a=43

=> 5a=43

=> a=43/5----(3)

(3) in (1):

b=20+2a

=> 20-2×(43/5)

=> 100-86/5

=> b=14/5.