The roots of the quadratic equation px^2 − qx + r = 0, p ≠ 0 are

Question

The roots of the quadratic equation \(px^2 - qx + r =0, p \ne 0\) are

(A) \(\frac{q \pm \sqrt{q^2 - 4pr}}{2p}\)

(B) \(\frac{q \pm \sqrt{q^2+ 4pr}}{2p}\)

(C) \(\frac{-q \pm \sqrt{q^2 - 4pr}}{2p}\)

(D) \(\frac{-q \pm \sqrt{q^2 + 4pr}}{2p}\)

Answer 1

Correct option is (A) \(\frac{q \pm \sqrt{q^2 - 4pr}}{2p}\)

The roots of a quadratic equation \(a x^{2}+b x+c=0\) are

\(x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}\)

Therefore, the given quadratic equation \(p{x}{ }^{2}-q x+r=0\)

where,

\(a=p, b=-q \text { and } c=r\)

\(x=\frac{-(-q) \pm \sqrt{(-q)^{2}-4 \times p \times r}}{2 \times p}\)

\(=\frac{q \pm \sqrt{q^{2}-4 p r}}{2 p}\)