Question

factorise x square + 3 root 3 x minus 30

Answer 1

Answer:

x²+3√3x-30 = (x+5√3)(x-2√3)

Explanation:

Given quadratic expression :

x²+3√3x-30

splitting the middle term we get

= x² +5√3x-2√3x-30

= x²+5√3x-2√3x-2√3 × 5√3

= x(x+5√3)-2√3(x+5√3)

= (x+5√3)(x-2√3)

Therefore,

x²+3√3x-30 = (x+5√3)(x-2√3)

•••••

Answer 2

$\bold{(x+5\sqrt{3})(x-2\sqrt{3})}$  are the factors of the quadratic equation  $\bold{x^2+3\sqrt{3}x-30=0}$

Given:

$x^2+3\sqrt{3}x-30=0$

To find:

The factors of $x^2+3\sqrt{3}x-30$ = ?

Solution:

To find the roots of the given quadratic equation split the terms in to sum of the terms given.

Then take the common terms and find the factors.

$x^2+3\sqrt{3}x-30=0$

$x^2+5\sqrt{3}x-2\sqrt{3}  x-30=0$  

$x(x+5\sqrt{3} )-2\sqrt{3}(x+5\sqrt{3} )=0$

$(x+5\sqrt{3} )(x-2\sqrt{3} )=0$

The value of x are $-5\sqrt{3} ,2\sqrt{3}$

Therefore, by the factorization method the roots $\bold{(x+5\sqrt{3})(x-2\sqrt{3})}$ are the roots of the quadratic equation $\bold{x^2+3\sqrt{3}x-30}$.