Question

if x+a is a factor of 2x square + 2ax + 5x + 10 find a

Answer 1

The value of a in from $\bold{2 x^{2}+2 a x+5 x+10}$  is 2.

Solution:

Given:

Since x+a is the factor of given equation, we can take x = -a.

Substitute the value of x in the polynomial equation, $2 x^{2}+2 a x+5 x+10$  

By substituting the value of x in above equation we get,

$\begin{array}{l}{2 a^{2}-2 a^{2}-5 a+10=0} \\ \\{-5 a+10=0} \\ \\{-5 a=-10} \\ \\{a=\frac{10}{5}}\end{array}$

Therefore, a = 2.

Answer 2

Answer:

Value of a = 2

Explanation:

It is given that,

(x+a) is a factor of 2x²+2ax+5x+10

Let p(x) =2x²+2ax+5x+10

/* By factor theorem :

" If (x-a) is a factor of a polynomial p(x) , then p(a) = 0 " */

Here ,

(x+a) is a factor of p(x) then

p(-a) = 0

=> 2(-a)²+2a(-a)+5(-a)+10=0

=> 2a²-2a²-5a+10=0

=> -5a+10 = 0

=> -5a = -10

Divide each term by (-5), we get

=> a = 2

Therefore,

Value of a = 2

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