Question

If two roots of $4x^3-12x^2+9x-2=0$ are equal, then the roots are

• A. $\frac{1}{2},\frac{1}{2},2$
• B. $-\frac{1}{2},-\frac{1}{2},2$
• C. $\frac{1}{4},\frac{1}{4},1$
• D. $\frac{1}{4},\frac{1}{4},2$

Answer 1

The correct option is A $\frac{1}{2},\frac{1}{2},2$

The given equation is $4x^3-12x^2+9x-2=0$

One of the roots of the equation is $x=2$ as it satisfies the equation.

Let the other roots of the equation be $x_1$ and $x_2$

Now, we know that the sum of the roots in a cubic equation is given by

$x_1+x_2+x_3=\frac{-b}{a}$

Thus $x_1+x_2+2=\frac{-(-12)}{4}$

Or, $2x_1=3-2=1$

[Because $x_1=x_2$]

Thus $x_1=\frac{1}{2}$

Also, $x_2=\frac{1}{2}$

Thus the roots of the equation are $\frac{1}{2},\frac{1}{2},2$