Question

Assertion (A): The equation whose roots are squares of the roots of $x^3-2x^2-2x+3=0$ is $x^3-8x^2+16x-9=0$.
Reason (R): The equation whose roots are the square of the roots of $f\left(x\right)=0$ is $f\left(\sqrt{x}\right)=0$.

• A. Both A and R are true and R is the correct explanation of A
• B. Both A and R are true and R is not the correct explanation of A
• C. A is true but R is false
• D. A is false but R is true

Answer 1

The correct option is A Both A and R are true and R is the correct explanation of A

Assertion:

Replacing $x$ by $\sqrt{x}$ in

$x^3-2x^2-2x+3=0,$ we get

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

$\Rightarrow x\sqrt{x}-2\sqrt{x}=2x-3$

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

$\Rightarrow x^3+4x-4x^2=4x^2=4x^2+9-12x$

$\Rightarrow x^3-8x^2+16x-9=0$

Hence, assertion is true by using reason.