Question

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

Answer 1

x+a is a factor of 2x²+2ax+5x+10
therefore f(-a)=0;
substituting values,
2(-a)²+2(a)(-a)+5(-a)+10=0
2a²-2a²-5a+10=0
-5a+10=0
therefore a=2

Answer 2

Answer:

The value of a is termed to be 2.

Solution:

Given that

$2 x ^ { 2 } + 2 a x + 5 x + 10$

Divide the $2 x ^ { 2 } + 2 a x + 5 x + 10$ by $x+a$

By using the division method, we get the remainder as 10-5a

$\begin{array} { l } { 10 - 5 a = 0 } \\\\ { 5 a = 10 } \\\\ { \therefore a = 2 } \end{array}$

Another method:

We can also find the value of a by this method,  

Let $x+a=0$

$x=-a$

Substitute the value of x in the given equation,

$\begin{array} { c } { 2 \mathrm { x } ^ { 2 } + 2 \mathrm { ax } + 5 \mathrm { x } + 10 = 0 } \\\\ { 2 ( - \mathrm { a } ) ^ { 2 } + 2 \mathrm { a } ( - \mathrm { a } ) + 5 ( - \mathrm { a } ) + 10 = 0 } \\\\ { 2 a ^ { 2 } - 2 a ^ { 2 } - 5 a + 10 = 0 } \\\\ { - 5 a + 10 = 0 } \end{array}$

$\begin{array} { c } { - 5 a = - 10 } \\\\ { 5 a = 10 } \\\\ { a = \frac { 10 } { 5 } = 2 } \end{array}$

Thus, we can find the value of a=2 in this method also.