Question

The difference between the roots of the quadratic equation x² + cx = 0 is 6. Find c.

a) 3
b) 6
c) -3
d) -6

Answer 1

The difference between the roots of the quadratic equation can be found by using the quadratic formula. By substituting the given value into the formula, we can calculate the value of c. In this case, the value of c is approximately 2.449.

Step-by-step explanation:

The difference between the roots of the quadratic equation can be found using the quadratic formula. The general form of a quadratic equation is ax² + bx + c = 0. In this case, we have x² + cx = 0. To find the difference between the roots, we can substitute the values into the formula and solve for c.

Using the quadratic formula, c can be calculated as:

c = (-b ± √(b² - 4ac)) / 2a

In this case, the difference between the roots is given as 6. By substituting this value into the quadratic formula, we can find the value of c.

Simplifying the equation, we have:

c = (-0 ± √(0² - 4(1)(-6))) / 2(1)

c = ± √(24) / 2

c = ± √6

Since the difference between the roots is positive, we choose the positive value for c. Therefore, c = √6, which is approximately 2.449.