Question

solve the problem please ​

Answer 1

SOLUTION

Let p(x)=

$2x {}^{3} + 3 {x}^{2} + ax + b$

As we know by remainder theorem.

Remainder of p(x) when divided by x-2= 0

=) x= 2 means p(2)

So,

$= > p(2) =2(2) {}^{3} + 3(2) {}^{2} + a(2) + b$

=) p(2)= 16+12+2a+b

Also, it is Given that p(2) = 2 substituting the value

=) 2=28+2a+b

=) 2a+b= -26...............(1)

Similarly,

Remainder of p(x) when divided by x+2=0

Remainder of p(x) when divided by x+2=0=) x= -2 means p(-2)

=) p(-2)= 2(-2)^3 +3(-2)^2 + a(-2) +b

=) p(-2)= -16+12-2a+b

Also, it is given that p(-2) = -2 on substitute the value above, we get

=) -2= -4-2a+b

=) -2a+b= 2..............(2)

On solving the above two eq^n (1) and (2)

Subtract the Equation (1)-(2)

=) 2a+b= -26

=) -2a +b = 2

+ - -

_________________

=) 4a= -28

=) a= -7

so,

putting the value of a in eq^n (1)

=) 2a+b= -26

=) 2(-7) +b= -26

=) -14 +b= -26

=) b= -26+14

=) b= -12

a= -7 & b= -12

HOPE it helps ✔️