Question

If the polynomials x2+ax2+5and x2-2x2+a are divided by (x+2) leave the same remainder,find the value of a

Answer 1

Given f(x) = x^2 + ax^2 + 5.

Given g(x) = x^2 - 2x^2 + a.

According to remainder theorem, when f(x) and g(x) is divided by x - a, the remainder is f(a).

Now,

(1)

When f(x) is divided by x+2, remainder is f(-2).

f(-2) = (-2)^2 + a(-2)^2 + 5

= 4 + 4a + 5

= 4a + 9

(2)

When g(x) is divided by x + 2, the remainder is f(-2).

g(-2) = (-2)^2 - 2(-2)^2 + a

= 4 - 8 + a

= -4 + a

Given that they leave the same remainder.

= > f(-2) = g(-2)

= > 4a + 9 = -4 + a

= > 3a = -13

= > a = -13/3.

Therefore, the value of a = -13/3.

Hope this helps!

Answer 2

Heya!!☻

Here's your answer !!!
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Let the given polynomial be f(x) = x²+ax²+5

g(x) = x²-2x²+a

Given that when f(x) and g(x) are divided by the (x+2) we get the same remainder.

That is f(2) = g(2)

Put x=2 in both f(x) and g(x)

(2)²+a(2)²+5 = (2)²-2(2)²+a

= 4+4a+5 = -4-8+a
= 9+4a = -13+a
= 3a = -13

so, a = 13/3
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Glad help you,
it helps you
thank you ☻

@vaibhav246