Question

If a and b are the roots of the equation $x^2-1=0$ the form of quadratic equation whose roots are 2a and 2b will be-

• A. $x^2-4\sqrt{2}=0$
• B. $x^2+4=0$
• C. $x^2-4=0$
• D. $x^2+4\sqrt{2}=0$

Answer 1

The correct option is C $x^2-4=0$

$\Rightarrow$ $a$ and $b$ are roots of the quadratic equation

$x^2-1=0$

So, $x^2-1=0$

$\Rightarrow$ $x^2=1$

$\therefore$ $x=\pm 1$

Let $a=+1$ and $b=-1$

Then, $2a=2$ and $2b=-2$

The required quadratic equation,

$(x-2a)(x-2b)=0$

$\Rightarrow$ $(x-2)(x+2)=0$

$\Rightarrow$ $x^2+2x-2x-4=0$

$\therefore$ $x^2-4=0$

The required quadratic equation is $x^2-4=0$.