Write two different quadratic equations?

Question

such that the sum of its roots is -2 and the product of its roots is 24 .what type of roots does this equation have and how do you know ?

Answer 1

The quadratic equation ax² + bx + c = 0

Sum of roots = -b/a

Product of roots = c/a

-b/a = - 2

b/a = 2

and c/a = 24

The equation ax² + bx + c = 0

a[ x² + (b/a)x + (c/a)] = 0

x² + (b/a)x + (c/a) = 0

Substitute the values of (b/a) and (c/a).

x² + 2x + 24 = 0

Compare it to ax² + bx + c = 0

a = 1, b = 2, c = 24

b² - 4ac = (2)² - 4(1)(24) = 4 - 96 = - 92

When b² - 4ac < 0, so this equation has no real roots.

The roots are imaginary.

To get different quadratic equations for a given a, b and c, ax² + bx + c = 0 is equivalent to for kax² + kbx + kc = 0 (where k is an integer).

In this case the equation is x² + 2x + 24 = 0

Multiply each side by 2.

2x² + 4x + 48 = 0

Two different quadratic equations are x² + 2x + 24 = 0 and 2x² + 4x + 48 = 0.