Question

Let $a$ and $b$ are non-zero real numbers and $\alpha^3+\beta^3=- a , \alpha \beta= b$, then the quadratic equation whose roots are $\frac{\alpha^2}{\beta}, \frac{\beta^2}{\alpha}$ is

• A. $a x^2+b x+a^2=0$
• B. $b x^2-a x+b^2=0$
• C. $b x^2+a x+b^2=0$
• D. $a x^2-b x+a^2=0$

Answer 1

Answer: (C)

$ \alpha^3+\beta^3=-a, \alpha \beta=b$
Now, $\frac{\alpha^2}{\beta}+\frac{\beta^2}{\alpha}=\frac{- a }{ b } ; \alpha \beta= b$
Equation of $x^2-\left(\frac{-a}{b}\right) x+b=0 \Rightarrow b x^2+4 x+b^2=0$