Question

prove that x+root 3 is a factor of 2root2x^2 + 5x + root 2

Answer 1

Answer:

To prove :

X-√3

is a factor of

$2 \sqrt{2} x {}^{2} + 5x + \sqrt{2}$

Answer

X+√3=0

X=-√3

putting this value in the above equation ,if the result is 0 then it is a factor of the equation

[tex]2 \sqrt{2} ( \sqrt{-3} ) {}^{2} + 5 (\sqrt{-3} ) + \sqrt{2} \\ = -6 \sqrt{2} - 5 \sqrt{3} + \sqrt{2} \\

=-5√2+5√3

The result is ≠0

hence it is not the factor of the equation

Answer 2

$\huge\bigstar\mathfrak\blue{\underline{\underline{SOLUTION}}}$

Given,

x+√3 is a factor of 2√2x^2+ 5x+√2

So,

x+√3= 0

=) x= -√3

(x-a) is the factor of f(x) if f(a)=0

Putting the value of x in above the equation;

$f( - \sqrt{3} ) = 2 \sqrt{2} ( - \sqrt{3} ) {}^{2} + 5( - \sqrt{3} ) + \sqrt{2} \\ \\ = > 2 \sqrt{2} \times 3 - 5 \sqrt{3} + \sqrt{2} \\ \\ = > 6 \sqrt{2} - 5 \sqrt{3} + \sqrt{2} \\ \\ = > 7 \sqrt{2} - 5 \sqrt{3}$

(x+√3) isn't the factor of this equation.

hope it helps ☺️