Question

While finding the roots of the quadratic equation 3$x^2$- 2$\sqrt{6}$ x + 2 = 0 using factorization method, the given equation is reduced to the form (ax+b)(cx+d). The value of (a $\times$ c)

• A.
• B. 3
• C. - ,
• D. 0

Answer 1

The correct option is B

3

In a$x^2$+bx+c=0, find 2 numbers p,q such that p+q = b and pq = (a $\times$ c)

3$x^2$- 2$\sqrt{6}$x +2 = 0

We need to split the middle term,

We can write as 3$x^2$- $\sqrt{6}$x- $\sqrt{6}$x + 2=0

Take the common terms out

$\sqrt{3}$x( $\sqrt{3}$x- $\sqrt{2}$)- $\sqrt{2}$($\sqrt{3}$x- $\sqrt{2}$ )=0

⇒( $\sqrt{3}$x- $\sqrt{2}$) ( $\sqrt{3}$x- $\sqrt{2}$ )=0

So the roots can be found out by equating the factors to zero.

Therefore the roots will be x=$\sqrt{\left(\frac{2}{3}\right)}$ , $\sqrt{\left(\frac{2}{3}\right)}$

Comparing the roots of x with (ax+b)(cx+d), we get a=$\sqrt{3}$ , c =$\sqrt{3}$

Therefore, ac = $\sqrt{3}\times \sqrt{3}$ = 3