Question

If the quadratic equation lx² – mx + n = 0 has roots which are reciprocal of each other, then which of the following is true?

Options

• l = n

• l = m

• m = n

• `l = 1/n`

Answer 1

l = n

Explanation:

1. Identify roots property

Let the roots of the quadratic equation lx² – mx + n = 0 be α and β. Since the roots are reciprocals of each other, we can express them as:

`β = 1/α` or α · β = 1

2. Apply vieta’s formula

For any quadratic equation of the form ax² + bx + c = 0, the product of the roots is given by the ratio of the constant term to the leading coefficient:

Product of roots = `c/a`

3. Substitute coefficients

In the given equation lx² – mx + n = 0:

1. Leading coefficient (a) = l
2. Constant term (c) = n

Substituting these into the product formula:

`α · β = n/l`

4. Solve for the condition

Since we know the product must be 1:

`1 = n/l`

Multiplying both sides by l, we get:

l = n