Question

The roots of the quadratic equation $x^2 - 3x - 10 = 0$ are:

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

Hint:

To find the roots of a quadratic equation by factorization, find two numbers that multiply to give the constant term and add to give the coefficient of $x$.

Answer 1

The Correct Option is B

Step 1: Write the given quadratic equation.
\[ x^2 - 3x - 10 = 0 \]
Step 2: Factorize the quadratic expression.
We need two numbers whose product is $-10$ and sum is $-3$.
These numbers are $-5$ and $2$.

Step 3: Split the middle term.
\[ x^2 - 5x + 2x - 10 = 0 \] \[ x(x - 5) + 2(x - 5) = 0 \]
Step 4: Factor out the common term.
\[ (x - 5)(x + 2) = 0 \]
Step 5: Solve for $x$.
\[ x - 5 = 0 \quad \text{or} \quad x + 2 = 0 \] \[ x = 5 \quad \text{or} \quad x = -2 \]
Step 6: Conclusion.
Hence, the roots of the quadratic equation are $5$ and $-2$.