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} \\ (b)/(a)\text{ and -}(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(7)/(6)`

That is

`1(1)/(6)\text{ and -1}(1)/(6)`