Question

If $3p^2=5p+2$ and $3q^2=5q+2$ where $n\ne q,$ then the equation whose roots are $3p-2q$ and $3q-2p$ is:

• A. $5x^2-3x-100=0$
• B. $5x^2+3x+100=0$
• C. $3x^2-5x+100=0$
• D. $3x^2+5x-100=0$
• E. $3x^2-5x-100=0$

Answer 1

Answer: (E)

Given that, $3p^2-5p-2=0$ $\Rightarrow$ $(3p+1)(p-2)=0$ $\Rightarrow$ $p=-\frac{1}{3},2$ and $3q^2-5q-2=0$ $\Rightarrow$ $(3q+1)(q-2)=0$ $\Rightarrow$ $q=\frac{-1}{3},2$ Since, $p\ne q\Rightarrow p=-\frac{1}{3},q=2$ Now, $(3p-2q)=-1-4=-5$ and $(3p-2p)=6+\frac{2}{3}=\frac{20}{3}$ $\therefore$ Equation is $x^2-\left(-5+\frac{20}{3}\right)x+\frac{(-5)(20)}{3}=0$ $\Rightarrow$ $3x^2-5x-100=0$