Question

Which are the solutions of the quadratic equation? x² = 7x 4 o

a) (- 7 - sqrt(65))/2,
b) (- 7 sqrt(65))/2 o -7,
c) 0 o (7 - sqrt(65))/2,
d) (7 sqrt(65))/2 o 7,0

Answer 1

To find the solutions of the quadratic equation x² = 7x, it can be written in standard form and solved either by factoring or using the quadratic formula, resulting in two solutions: x = 0 or x = 7.

Step-by-step explanation:

The quadratic equation given by the student, x² = 7x, can be rewritten in the standard form ax² + bx + c = 0 by bringing all terms to one side, which gives us x² - 7x = 0. Solving this equation directly or using the quadratic formula, the solutions or roots can be found. Since the equation is factorable, we can solve it by factoring x out: x(x - 7) = 0, which gives us two solutions: x = 0 or x = 7.

Alternatively, if we apply the quadratic formula x = (-b ± √(b² - 4ac)) / (2a) to the equation x² - 7x = 0, where a = 1, b = -7, and c = 0, we obtain:
x = (7 ± √((-7)² - 4(1)(0))) / (2(1))
x = (7 ± √(49)) / 2
x = (7 ± 7) / 2
This yields the same solutions: either x = 0 or x = 7.