the polynomials (2x cube + x square - ax + 2) and (2x cube - 3x square - 3x + a) when divided by (x-2) leave the same remainder.find the value of a.
the polynomials (2x cube + x square - ax + 2) and (2x cube - 3x square - 3x + a) when divided by (x-2) leave the same remainder.find the value of a.
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
Answer:
Value of a is 8.
Step-by-step explanation:
let, p(x) = 2x³ + x² - ax + 2
g(x) = 2x³ - 3x² - 3x + a
To find : Value of a when p(x) & g(x) divided by x - 2 leaves the same remainder.
We use remainder theorem,
Remainder Theorem states that When a polynomial p(x) is divided by a polynomial x - a then the remainder is p(a).
So, Remainder when p(x) divided by x - 2
Remainder we get ,
p(2) = 2(2)³ + (2)² - a(2) + 2
= 2 × 8 + 4 - 2a + 2
= 22 - 2a ...............(1)
Remainder when g(x)is divided by x - 2
g(2) = 2(2)³ - 3(2)² - 3(2) + a
= 2 × 8 - 3 × 4 - 6 + a
= a - 2 .........................(2)
We are given (1) = (2)
p(2) = g(2)
22 - 2a = a - 2
3a = 24
a = 8
Therefore, Value of a is 8.