Question

read the following into factors 4x^2 - 12 x + 9​

Answer 1

4x square - 12x+ 9
4x square-6x-6x+9
2x(2x-3) -3(2x-3)
( 2x- 3)= 0
x = 3/2

Answer 2

$\large \underline{\textbf{Answer}}$

$\sf{Let\: p(x)} = 4 x^2 \:- 12x + 9$

Now we can solve this quadratic equation by 3 or more methods like=>

1)Middle term break method

2)Completing Square method and

3)By using Quadratic formula.

Here we will solve the quadratic equation by Quadratic formula method=>

$p(x) = 4x^2 - 12x + 9$

So,$D=b^2 - 4\times a\times \times c$

$\impliesD=(-12)^2 - 4\times 4 \times 9$

=>D = 144 - 144

       =>D = 0.

Since,d=0 hence the equation will have two equal and real roots.

Now,we have =>

$\implies x =\dfrac{-b\pm\sqrt{d}}{2a}$

$\implies x=\dfrac{12 \pm\sqrt{0}}{2*4}$

$\implies x = \dfrac{12}{8}$

Hence

the roots of the equation are $\dfrac{3}{2}$ or  $\dfrac{3}{2}$

Remember

In quadratic formula

$X=\dfrac{-b\pm\sqrt{d}}{2a}$

and

d is discriminant which determines nature of roots