Question

if (x+a) is a factor of 2x^2+2ax+5x+10, find a​

Answer 1

Answer:

a = 2

Explanation:

if x + a is a factor of 2x^2+2ax+5x+10 then on substituting x +a = 0

or x = - a in equation the result will be 0.

Now put values

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

2a^2 - 2a^2 -5a=-10

5a=10

a = 10/5

a = 2.

or see picture.

Answer 2

$here \: the \: factor \: is \: \\ x + a = 0 \\ x = - a \\ now \: we \: put \: the \: value \: of \: x \: in \: the \: equation \: \\ 2x {}^{2} + 2ax + 5x + 10 = 0 \\ 2( - a) {}^{2} + 2 \times a \times ( - a) + 5 \times ( - a) + 10 = 0 \\ 2a {}^{2} - 2a {}^{2} - 5a + 10 = 0 \\ - 5a + 10 = 0 \\ - 5a = - 10 \\ 5a = 10 \\ a = 10 \div 5 \\ a = 2 \: \: \: \: \: \: answer \\ \\ i \: hope \: that \: helps \: you$