Question

The roots of the quadratic equation \( px^2 - qx + r = 0 \), where \( p \neq 0 \), 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. \( \frac{-q \pm \sqrt{q^2 + 4pr}}{2p} \)

Hint:

The quadratic formula is derived from completing the square of \( ax^2 + bx + c = 0 \).

Answer 1

The Correct Option is A

Step 1: Use the quadratic formula For a quadratic equation of the form \( ax^2 + bx + c = 0 \), the roots are given by: \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] Step 2: Apply the formula Here, comparing with \( px^2 - qx + r = 0 \): - \( a = p \) - \( b = -q \) - \( c = r \) Substituting into the quadratic formula: \[ x = \frac{-(-q) \pm \sqrt{(-q)^2 - 4(p)(r)}}{2p} \] \[ = \frac{q \pm \sqrt{q^2 - 4pr}}{2p} \] Thus, the correct answer is: \[ \frac{q \pm \sqrt{q^2 - 4pr}}{2p} \]