Question

For what value of \( p \) will the equation \( px^2 - 2x + 3 = 0 \) have real and equal roots?

• A. \( 1 \)
• B. \( \frac{1}{3} \)
• C. \( 3 \)
• D. \( \frac{1}{2} \)

Hint:

For a quadratic equation to have real and equal roots, the discriminant must be zero: \[ b^2 - 4ac = 0 \]

Answer 1

The Correct Option is B

For real and equal roots, the discriminant must be zero:
\[ D = b^2 - 4ac = 0 \] Here,
\[ b = -2, \quad a = p, \quad c = 3 \] \[ (-2)^2 - 4(p)(3) = 0 \] \[ 4 - 12p = 0 \] \[ 12p = 4 \] \[ p = \frac{1}{3} \]