Solve the equation 3x 2 4x 5 0 - JAMB Mathematics 2024 Question

To solve the quadratic equation \( 3x^2 - 4x - 5 = 0 \), we will use the quadratic formula:

The quadratic formula is given by:

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

In the equation \( 3x^2 - 4x - 5 = 0 \), the coefficients are:

• a = 3
• b = -4
• c = -5

Now, substitute the values of \( a \), \( b \), and \( c \) into the quadratic formula:

\( x = \frac{-(-4) \pm \sqrt{(-4)^2 - 4(3)(-5)}}{2(3)} \)

\( x = \frac{4 \pm \sqrt{16 + 60}}{6} \)

\( x = \frac{4 \pm \sqrt{76}}{6} \)

Now, calculate the square root of 76:

\( \sqrt{76} \approx 8.7178 \)

Thus, the equation becomes:

\( x = \frac{4 \pm 8.7178}{6} \)

Now, solve for both values of \( x \):

1) For \( x_1 = \frac{4 + 8.7178}{6} \):

\( x_1 = \frac{12.7178}{6} \approx 2.12 \)

2) For \( x_2 = \frac{4 - 8.7178}{6} \):

\( x_2 = \frac{-4.7178}{6} \approx -0.79 \)

Therefore, the solutions to the equation are \( x = 2.12 \) or \( x = -0.79 \)