Question

Find the number of rational roots of the quadratic equation $(x^2-2{)}^2\times (x^3-8{)}^2\times (x^2-16{)}^2=0$

• A. 7
• B. 3
• C. 5
• D. 4

Answer 1

The correct option is B

3

This equation is true when $(x^2-2{)}^2=0$ or $(x^3-8{)}^2=0$ or $(x^2-16{)}^2=0$.
$(x^2-2{)}^2=0;x=\sqrt{2}$ (Irrational)
$(x^3-8{)}^2=0;x=2$ (Rational)
$(x^2-16{)}^2=0;x=\pm 4$ (Rational)
So, there exist 3 rational roots.