Question

find the value of a if( x-1) is a factor of (2x)2+ax+root2

Answer 1

By factor theorem


$p(x) = 2 {x}^{2} + ax + \sqrt{2}$

$p(1) = 2 {(1)}^{2} + a(1) + \sqrt{2}$

$0 = 2 + a + \sqrt{2}$

$a = - 2 - \sqrt{2}$

Answer 2

If x - 1 is a factor of
$2 {x}^{2} + ax + \sqrt{2 } \\ then \: \: \:$
x - 1 = 0
and x = 1
Now, after substituting the value of x in the above equation, we'll get

2 (1)^2 + a (1) + root 2 = 0
= 2 + a + root 2 = 0
$= 2 + a + \sqrt{2} = 0 \\ = a = - (2 + \sqrt{2} )$
Thankyou.....