Question

If the roots of the quadratic equation \(px^2+qx+r=0\), are equal, then \(q^2 =\)

• A. 2 pr
• B. 3 pr
• C. 4 pr
• D. 8 pr

Answer 1

The Correct Option is C

Step 1: For a quadratic equation of the form \( ax^2 + bx + c = 0 \), the condition for equal roots is that the discriminant is zero.

Step 2: The discriminant is given by:
\[ D = b^2 - 4ac \]
Step 3: In the given equation, compare with standard form:
\( a = p,\ b = q,\ c = r \)

Step 4: Apply the condition for equal roots:
\[ D = q^2 - 4pr = 0 \]
\[ \Rightarrow q^2 = 4pr \]
Step 5: Hence, the value of \( q^2 \) is \( 4pr \)

The correct option is (C): \(4 pr\)