Question

If the product of the roots of the quadratic equation \( x^2 - 5x + p = 10 \) is -4, then the value of \( p \) is:

• A. \( 4 \)
• B. \( 5 \)
• C. \( 6 \)
• D. \( 8 \)

Hint:

The product of roots of a quadratic equation \( ax^2 + bx + c = 0 \) is given by: \[ \alpha \beta = \frac{c}{a}. \]

Answer 1

The Correct Option is C

For a quadratic equation \( ax^2 + bx + c = 0 \):
- Product of roots: \( \alpha \beta = \frac{c}{a} \).
Given: \[ \alpha \beta = -4, \quad a = 1, \quad c = p. \] \[ \frac{p}{1} = -4 \Rightarrow p = -4. \] Since the equation is given as \( x^2 - 5x + p = 10 \), we solve for \( p \): \[ p = -4 + 10 = 6. \]