Let $$\alpha \ne \beta $$ and $${\alpha ^2} + 3 = 5\alpha $$ while $${\beta ^2} = 5\beta - 3.$$ The quadratic equation whose roots are $$\frac{\alpha }{\beta }$$ and $$\frac{\beta }{\alpha }$$ is
A.
$$3{x^2} - 31x + 3 = 0$$
B.
$$3{x^2} - 19x + 3 = 0$$
C.
$$3{x^2} + 19x + 3 = 0$$
D.
None of these
Answer :
$$3{x^2} - 19x + 3 = 0$$
Solution :
Clearly $$\alpha ,\beta $$ are the roots of the equation $${x^2} - 5x + 3 = 0.$$ Use $$\alpha + \beta = 5,\alpha \beta = 3.$$
Releted MCQ Question on Algebra >> Quadratic Equation
Releted Question 1
If $$\ell ,m,n$$ are real, $$\ell \ne m,$$ then the roots by the equation: $$\left( {\ell - m} \right){x^2} - 5\left( {\ell + m} \right)x - 2\left( {\ell - m} \right) = 0$$ are