Question

Factorise form of 4x2 – 12x + 9 is
(a)(x-3)(2x-3)
(b) (x+3)(2x-3)
(C) (2x-3)(2x+3)
(d) (2x-3)(2x-3)​

Answer 1

Answer: OPT D

Step-by-step explanation:

4x2-12x+9

Explanation:Multiply the two outer coefficients.

4⋅9=36

Find two numbers, that when multiplied equal 36, and when added equal -12.

-6 and -6.

−6+−6=12

−6⋅−6=36

Rewrite the equation with the x value replaced by the two new values.

4x2−6x−6x+9

Seperate the equation into two parts.

4x2−6x and −6x+9

Find the GCF of the two parts.

2x(2x−3) and −3(2x−3)

Take the GCF as your first factor, and the two remaining values as the second.

2x-3 and 2x-3

Ans opd d

Mark me brainlieat

Answer 2

Given: The equation is$4x^{2} -12x+9=0$.

We have to solve the above equation in factorized form.

We are solving in the following way:

$\text { To factor the quadratic function } 4 x^{2}-12 x+9, \text { we should solve the corresponding \\quadratic }\\\text { equation } 4 x^{2}-12 x+9=0$$\text { Indeed, if } x_{1} \text { and } x_{2} \text { are the roots of the quadratic equation } a x^{2}+b x+c=0, \text { then }\\a x^{2}+b x+c=a\left(x-x_{1}\right)\left(x-x_{2}\right)$

  $\text { Solving the quadratic equation } 4 x^{2}-12 x+9=0 \text {. }\\\text { In our case, } a=4, b=-12, c=9 \text {. }\\\text { Now, find the discriminant using the formula } D=b^{2}-4 a c: D=(-12)^{2}-4 \cdot 4 \cdot 9=0 \text {. }$

$\text { Since the discriminant is zero, there is one root of multiplicity } 2 \text { (occurs two times). }\\\text { To find it, use the formula } x=\frac{-b}{2 a}: x=\frac{-(-12)}{2 \cdot 4}=\frac{3}{2}$$\text { The roots are } x_{1}=\frac{3}{2}, x_{2}=\frac{3}{2}$

$\text { We have one root of multiplicity } 2 \text {, so } 4 x^{2}-12 x+9=4\left(x-\frac{3}{2}\right)^{2} \text {. }\\\left(4 x^{2}-12 x+9\right)=\left(4\left(x-\frac{3}{2}\right)^{2}\right)$

$\text { Therefore, } 4 x^{2}-12 x+9=4\left(x-\frac{3}{2}\right)^{2} \text {. }$

Solving the above equation further we get,

$4 x^{2}-12 x+9=(2 x-3)^{2}$

Hence, after solving the above equation in the factorized form we get,

$4 x^{2}-12 x+9=(2 x-3)(2x-3)$.

And option d) is the correct answer.