Question

If p, q and r are rational numbers and p ≠ q ≠ r, then roots of the equation (p² – q²)x² – (q² – r²)x + (r² – p²) = 0 are:

Options

• `"p"/"q", "r"/"p"`

• `"p"^2/"q"^2, "r"^2/"q"^2`

• `1, ("p"^2 - "q"^2)/("r"^2 - "p"^2)`

• `-1, ("p"^2 - "r"^2)/("p"^2 - "q"^2)`

Answer 1

`-1, ("p"^2 - "r"^2)/("p"^2 - "q"^2)`

Explanation:

Putting x = – 1, we have

(p² – q²)(–1)² – (q² – r²)(–1) + (r² – p²)

⇒ p² – q² + q² – r² + r² – p² = 0

∴ x = –1 is one root.