Question

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QUESTION :

If (x + a) is a factor of 2x2 + 2ax + 5x + 10 find a.

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Answer 1

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Given (x + a) is a factor of f ( x ) = 2 x 2 + 2 a x + 5 x + 10 . Let us now divide by x + a . Hence, the value of a is 2 .

Answer 2

Appropriate Question:-

• If (x + a) is a factor of 2x² + 2ax + 5x + 10 find a.

Given:-

• (x + a) is a factor of 2x² + 2ax + 5x + 10

To Find:-

• a

Solution:-

let f(x) = 2x² + 2ax +5x+10

$g(x)=x+a \\ \\ x+a=0 \\ \\ x=−a$

$\dashrightarrow \: f( - a) \\ = 2( - a ){}^{2} + 2a( - a) + 5a + 10 \\ \\ \\ \dashrightarrow \: 2 {a}^{2} - {2a}^{2} - 5a + 10 = 0 \\ \\ \\ \dashrightarrow \: \: 5a + 10 = 0 \\ \\ \\ \dashrightarrow \: 5a = 10 \\ \\ \\ \dashrightarrow \: a = \frac{10}{5} \\ \\ \color{lime} \therefore\boxed {a = 2}$