Which of the following is a solution to the quadratic equation 2x² - 9x = 4?
• X = -0.77
• X = 4.77
• X = -0.91
• X = 4.91
The solution to the quadratic equation 2x² - 9x = 4 can be found by setting the equation equal to 0:
2x² - 9x - 4 = 0.
To solve this equation, we can use factoring, completing the square, or the quadratic formula. Let's use the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a).
In this case, a = 2, b = -9, and c = -4. Substituting these values into the quadratic formula, we get:
x = (9 ± √((-9)² - 4 * 2 * (-4))) / (2 * 2)
= (9 ± √(81 + 32)) / 4
= (9 ± √113) / 4.
So the solutions for x are:
x = (9 + √113) / 4
x = (9 - √113) / 4.
Therefore, none of the given options (X = -0.77, X = 4.77, X = -0.91, X = 4.91) is a solution to the quadratic equation 2x² - 9x = 4.