Question

Which of the following quadratic polynomials has zeros \( \frac{3}{5} \) and \( -\frac{1}{2} \)?

• A. \( 10x^2 + x + 3 \)
• B. \( 10x^2 + x - 3 \)
• C. \( 10x^2 - x + 3 \)
• D. \( 10x^2 - x - 3 \)

Hint:

Use the standard quadratic form \( x^2 - (\alpha + \beta)x + \alpha \beta = 0 \) to construct equations from given roots.

Answer 1

The Correct Option is D

The quadratic equation with given roots \( \alpha \) and \( \beta \) is:
\[ x^2 - (\alpha + \beta)x + \alpha \beta = 0. \] \[ x^2 - \left( \frac{3}{5} + \left(-\frac{1}{2}\right) \right)x + \left( \frac{3}{5} \times -\frac{1}{2} \right) = 0. \] \[ x^2 - \left( \frac{6}{10} - \frac{5}{10} \right)x + \left( -\frac{3}{10} \right) = 0. \] \[ 10x^2 - x - 3 = 0. \]