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:

Use the sum and product of roots: \[ \alpha + \beta = -\frac{b}{a}, \quad \alpha \beta = \frac{c}{a} \]

Answer 1

The Correct Option is C

Using the sum and product of roots formula:
\[ \alpha + \beta = -\frac{b}{a}, \quad \alpha \beta = \frac{c}{a} \] For \( x^2 + x - 20 = 0 \):
\[ \alpha + \beta = -\frac{1}{1} = -1, \quad \alpha \beta = \frac{-20}{1} = -20 \] Since one root is \( 4 \):
\[ 4 + \beta = -1 \] \[ \beta = -5 \]