Quick Easy Simple Task

**Joker37** · March 6th 2009, 05:01 PM

Solve each of the following quadratic equation by factorising and applying the Null Factor Law.

2x^2 - 5 = 0

Please show complete steps!

**Prove It** · March 6th 2009, 05:25 PM

Originally Posted by Joker37

Solve each of the following quadratic equation by factorising and applying the Null Factor Law.

2x^2 - 5 = 0

Please show complete steps!

$2x^2 - 5 = 0$

$2\left(x^2 - \frac{5}{2}\right) = 0$

$2\left[x^2 - \left(\sqrt{\frac{5}{2}}\right)^2\right] = 0$

$2\left(x + \sqrt{\frac{5}{2}}\right)\left(x - \sqrt{\frac{5}{2}}\right) = 0$

So by Null Factor Law

$x + \sqrt{\frac{5}{2}} = 0$ or $x - \sqrt{\frac{5}{2}} = 0$

$x = -\sqrt{\frac{5}{2}}$ or $x = \sqrt{\frac{5}{2}}$ .

If you have to rationalise the denominator, you should end up with

$x = -\frac{\sqrt{10}}{2}$ or $x = \frac{\sqrt{10}}{2}$ .

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