Question

the polynomials ax^3+3x^2-13 and 2x^2-5x+a are divided by (x+2) leaves the same remainder in each case, find a

Answer 1

SOLUTION:-

Given:

The polynomials are ax³ +3x² -13 & 2x²-5x +a are divided by (x+2).

To find:

The value of a.

Explanation:

Let r(x)=ax³+3x² -13 & m(x)=2x² -5x +a be the given polynomials.

The remainder when r(x) & m(x) are divided by (x+2).

So,

x+2= 0

=) x= -2

According to the question:

r(-2) = m(-2)

=) a(-2)³ + 3(-2)² -13= 2(-2)² -5(-2) +a

=) a(-8) + 3(4) -13 = 2(4) -(-10) +a

=) -8a + 12 -13 = 8 +10 +a

=) -8a -1 = 18 +a

=) -8a -a = 18 +1

=) -9a = 19

=) a= 19/-9

Thus,

The value of a is -19/9

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