30. If polynomials ax + 3x - 3 and 2x - 5x + a leaves the same remainder when each is divided by
X-4, find the value of a
Answers
Answer :-
Value of a is - 7.
Explanation :-
Let
- f(x) = ax + 3x - 3
- p(x) = 2x - 5x + a
When f(x) divided by (x - 4)
Finding the zero of x - 4
x - 4 = 0
x = 4
By Remainder theorem f(4) is the remainder
When p(x) is divided by (x - 4)
Zero of x - 4 is 4
By remainder theorem p(4) is the remainder
Given
Remainder when f(x) is divided by (x - 4) = Remainder when p(x) is divided by (x - 4)
⇒ f(4) = p(4)
⇒ a(4) + 3(4) - 3 = 2(4) - 5(4) + a
⇒ 4a + 12 - 3 = 8 - 20 + a
⇒ 4a + 9 = - 12 + a
⇒ 4a - a = - 12 - 9
⇒ 3a = - 21
⇒ a = - 21/3
⇒ a = - 7
∴ the value of a is - 7.
•°• the value of a = - 7
Given :-
- ax + 3x - 3 = f (x)
- 2x - 5x + a = p (x)
- Divisor = x - 4
To find :-
- Value of a
Solution :-
When, x - 4 = 0
x = 4
By remainder theorem : When a polynomial, f(x), is divided by a linear polynomial, x - a, the remainder of that division will be equivalent to p (x)
•°• f (x) = p (x)
f (4) = p (4)
Substituting 4 for x in the polynomial,
ax + 3x - 3 = 2x - 5x + a
a(4) + 3(4) - 3 = 2(4) - 5(4) + a
4a + 12 - 3 = 8 - 20 + a
4a + 9 = - 12 + a
4a - a = - 12 - 9
3a = - 21
a =
•°• a = - 7