Question

If x+2 is a factor of 2x 2 +2ax +5x +10 , find a .

Answer 1

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Let f(x)=2x^2+2ax+5x+10

If x+a is a factor

f (-a)=0

f (- a)=2*((-a)^2)+2*a*(-a)+5*(-a)+10=0

2(a)^2-2(a)^2-5a+10=0

-5a+10=0

-5a=-10

5a=10

a =10/5=2

a =2

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Answer 2

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$<b><u><I>Let g(x) be ( x + 2) & p(x) be 2x ^2 + 2ax + 5x + 10.</b>$

Then g(x) = 0 = x + 2 . => x + 2 = 0 . Therefore x = -2.

And, g(x) will be a factor of p(x) if p(x)= 0.

Now , By substituting in p(x) , we get:

2 ×(-2)^2 + 2×a ×(-2) + 5 × (-2) + 10

= 2 × 4 + (-4a) + (-10) + 10.

= 8 - 4a - 10 + 10.

=8-4a.

So ATQ, 8 - 4a = 0.

or -4a = 0-8.

or -4a = -8.

or a = (-8/-4).

Therefore a = 2.

Therefore the value of a is 2.