Question

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
​

Answer 1

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.

Answer 2

$\bold{\underline{\underline{Answer:}}}$

•°• the value of a = - 7

$\bold{\underline{\underline{Step\:-\:by\:-\:step\:explanation:}}}$

Given :-

1. ax + 3x - 3 = f (x)
2. 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,

$\implies$ax + 3x - 3 = 2x - 5x + a

$\implies$ a(4) + 3(4) - 3 = 2(4) - 5(4) + a

$\implies$ 4a + 12 - 3 = 8 - 20 + a

$\implies$ 4a + 9 = - 12 + a

$\implies$ 4a - a = - 12 - 9

$\implies$ 3a = - 21

$\implies$ a = $\bold{\frac{-21}{3}}$

•°• a = - 7