Question

Factorise 3xsquare +5root5x -10=0​

Answer 1

We are given an equation 3x² + 5√5x - 10 = 0, and we have to factorize the equation.

So, for solving this question we'll be using the quadratic formula, i.e., $\text x=\dfrac{-\text b\pm\sqrt{\text{d}}}{2\text a}$

Here, a = 3, b = 5√5, c = -10,

So, first let's find the Discriminant, or d, i.e., $\text b^2-4\text{a}\text{c}$

Let's plug in the value and find the Discriminant;

$(5\sqrt{5})^2-4(3)(-10)$

Simplify;

$125 + 120 = 245$

So, we got the Discriminant as 245.

Now, let's plug in all the values in the quadratic formula;

$\text x=\dfrac{-5\sqrt{5}\pm\sqrt{245}}{2\times3}$

Simplify.

$\implies\text x=\dfrac{-5\sqrt{5}\pm\sqrt{245}}{6}$

$\implies\text x=\dfrac{-5\sqrt{5}\pm\sqrt{5\times49}}{6}$

$\text x=\dfrac{-5\sqrt{5}\pm7\sqrt{5}}{6}$

Now, as we have the "$\pm$" symbol in between. We'll have 2 cases;

Case 1:

If it is "+";

$\text x=\dfrac{-5\sqrt{5}+7\sqrt{5}}{6}$

$\implies \text x=\dfrac{2\sqrt{5}}{6} = \boxed{\dfrac{\sqrt{5}}{3}}$

And Case 2:

If it is "-"

$\text x=\dfrac{-5\sqrt{5}-7\sqrt{5}}{6}$

$\implies\text x=\dfrac{-12\sqrt{5}}{6}=\text x=\boxed{-2\sqrt{5}}$