Question

If one root of the quadratic equation \( x^2 + x - 20 = 0 \) is 4, then the other root is:

• A. \( 5 \)
• B. \( -4 \)
• C. \( -5 \)
• D. \( 3 \)

Hint:

The sum of the roots of a quadratic equation \( ax^2 + bx + c = 0 \) is given by \( -\frac{b}{a} \).

Answer 1

The Correct Option is C

Step 1: Use the sum of roots formula For a quadratic equation \( ax^2 + bx + c = 0 \), the sum of the roots is: \[ \alpha + \beta = -\frac{b}{a} \] Here, \( a = 1 \), \( b = 1 \), and \( c = -20 \). Step 2: Solve for the other root Given one root \( \alpha = 4 \): \[ 4 + \beta = -\frac{1}{1} \] \[ 4 + \beta = -1 \] \[ \beta = -5 \] Thus, the correct answer is \( -5 \).