Solve the equation $3x^2 − 4x − 5 = 0$

Analysis

To solve the quadratic equation $3x^2 - 4x - 5 = 0$, we need to find the values of $x$ that satisfy the equation. Since this equation does not factorize easily into simple integers, we use the Quadratic Formula.

Concept: The Quadratic Formula

For any quadratic equation in the form $ax^2 + bx + c = 0$, the solutions for $x$ are given by:

In your equation ($3x^2 - 4x - 5 = 0$):

• $a = 3$
• $b = -4$
• $c = -5$

Step-by-Step Solution

1. Substitute the values into the formula:

2. Simplify the terms:

• $-(-4) = 4$
• $(-4)^2 = 16$
• $-4 \times 3 \times -5 = 60$
• $2 \times 3 = 6$

So, the equation becomes:

3. Calculate the square root: $\sqrt{76} \approx 8.7178$

4. Solve for the two possible values of $x$:

• Case 1 (Addition): $x = \frac{4 + 8.7178}{6} = \frac{12.7178}{6} \approx 2.1196 \approx \mathbf{2.12}$

• Case 2 (Subtraction): $x = \frac{4 - 8.7178}{6} = \frac{-4.7178}{6} \approx -0.7863 \approx \mathbf{-0.79}$

Conclusion

Comparing our results ($x \approx 2.12$ or $-0.79$) with the given options, we find that they match option B.

Exam Tip

When you see a quadratic equation in a JAMB exam, always check the discriminant ($b^2 - 4ac$) first. If it is not a perfect square, you know immediately that the answer will involve decimals, and you should reach for the quadratic formula rather than trying to factorize by grouping!