Question

5) Factor the following special quadratics: a) x 24x+144 b) 36x² -49

Answer 1

Given a quadratic equation of the form

x² -2ax+a²,

Then the factor is x = a

Therefore,

x² -24x+144= x² -2(12)x+ 12²

Hence in this case a = 12

Then the factor is 12

b)

Given a quadratic equation of the form

$\begin{gathered} a^2x^2-b^2, \\ \text{Then the factor of the equation is} \\ \frac{b}{a}\text{ and -}\frac{b}{a} \\ \text{Where a and b are constants} \end{gathered}$

In this case,

$\begin{gathered} a^2=36\Rightarrow a=6 \\ b^2=49\Rightarrow b=7 \end{gathered}$

Therefore

The roots are

$\pm\frac{7}{6}$

That is

$1\frac{1}{6}\text{ and -1}\frac{1}{6}$