Question

The polynomials 2x - 7x2 + ax = 6 and x3 - 8r2 + (2a + Dt - 16 leave the same remainder when divided by t - 2. Find the value of 'a'​

Answer 1

Question:

The polynomials 2x - 7x2 + ax = 6 and x3 - 8r2 + (2a + Dt - 16 leave the same remainder when divided by t - 2. Find the value of 'a'​

Answer:

a = 10

Step-by-step explanation:

Let f(x) = 2x^3 − 7x^2 + ax − 6

Put x − 2 = 0

⇒x = 2

When f(x) is divided by (x−2), remainder = f(2)

∴f(2) = 2(2)^3 − 7(2)^2 + a.2 − 6

=2.8 − 7.4 + 2a − 6

=16 − 28 − 6 + 2a

=2a − 18

Let g(x) = x^3 − 8x^2 + (2a+1)x − 16

when g(x) is divided by (x−2) remainder =g(2)

∴g(2) = (2)^3 − 8(2)^2 + (2a+1)^2 − 16

= 8 − 32 + 4a + 2 − 16

= 4a − 38

By the condition we have

f(2) = g(2)

2a − 18 = 4a − 38

4a − 2a = 38 − 18

2a = 20

a = 20​/2

a = 10

∴ Thus, the value of a=10

Hope you understand.