When two roots of quadratic equation are α,\;1/α then what will be the quadratic equation:

Correct Answer is : αx2−(α2+1)x+α=0α x²-(α²+1)x+α=0αx2−(α2+1)x+α=0

Correct Answer is : αx2−(α2+1)x+α=0α x²-(α²+1)x+α=0αx2−(α2+1)x+α=0

Test Index

Equations

Question : 33 of 39

Marks: +1, -0

\alpha,\;\frac{1}{\alpha}

then what will be the quadratic equation:

Solution:

Concept:

For a quadratic equation with given roots, use the relation:

x^2 - (\text{sum of roots})x + (\text{product of roots}) = 0

Explanation:

Let the roots be

\alpha

and

\frac{1}{\alpha}

Sum of roots:

\alpha + \frac{1}{\alpha} = \frac{\alpha^2 + 1}{\alpha}

Product of roots:

\alpha \cdot \frac{1}{\alpha} = 1

The quadratic equation is

x^2 - \frac{\alpha^2 + 1}{\alpha}x + 1 = 0

Multiplying both sides by

\alpha

\alpha x^2 - (\alpha^2 + 1)x + \alpha = 0

Answer:

Comparing with the options, option A matches perfectly.

Go to Question:

Prev Question

Next Question