Solve each of the following quadratic equation by factorising and applying the Null Factor Law.
2x^2 - 5 = 0
Please show complete steps!
$\displaystyle 2x^2 - 5 = 0$
$\displaystyle 2\left(x^2 - \frac{5}{2}\right) = 0$
$\displaystyle 2\left[x^2 - \left(\sqrt{\frac{5}{2}}\right)^2\right] = 0$
$\displaystyle 2\left(x + \sqrt{\frac{5}{2}}\right)\left(x - \sqrt{\frac{5}{2}}\right) = 0$
So by Null Factor Law
$\displaystyle x + \sqrt{\frac{5}{2}} = 0$ or $\displaystyle x - \sqrt{\frac{5}{2}} = 0$
$\displaystyle x = -\sqrt{\frac{5}{2}}$ or $\displaystyle x = \sqrt{\frac{5}{2}}$.
If you have to rationalise the denominator, you should end up with
$\displaystyle x = -\frac{\sqrt{10}}{2}$ or $\displaystyle x = \frac{\sqrt{10}}{2}$.