Question

The roots of a quadratic equation \(x^2-3x-10=0\) are

• A. -5, 2
• B. 5, 2
• C. -2, 5
• D. -2, -5

Answer 1

The Correct Option is C

To solve the problem, we need to find the roots of the quadratic equation:
$ x^2 - 3x - 10 = 0 $

1. Understanding the Standard Form:

A quadratic equation is of the form:

$ ax^2 + bx + c = 0 $

Here, $ a = 1 $, $ b = -3 $, and $ c = -10 $

2. Using the Quadratic Formula:

The roots of a quadratic equation are given by:

$ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} $

Substituting the values:

$ x = \frac{-(-3) \pm \sqrt{(-3)^2 - 4(1)(-10)}}{2(1)} $

$ x = \frac{3 \pm \sqrt{9 + 40}}{2} $

$ x = \frac{3 \pm \sqrt{49}}{2} $

$ x = \frac{3 \pm 7}{2} $

3. Calculating the Two Roots:

$ x_1 = \frac{3 + 7}{2} = \frac{10}{2} = 5 $

$ x_2 = \frac{3 - 7}{2} = \frac{-4}{2} = -2 $

Final Answer:

The roots of the equation are $ {-2, \, 5} $