Question

Suppose a quadratic equation has the form x^2 + x + c = 0. Show that the constant c must be less than 1/4 in order for the equation to have two real solutions.

Answer 1

Answer:

see explanation

Step-by-step explanation:

Given a quadratic equation in standard form

ax² + bx + c = 0 ( a ≠ 0 )

Then for the equation to have 2 real roots , the discriminant must be greater than zero , that is

b² - 4ac > 0

x² + x + c = 0 ← is in standard form

with a = 1, b = 1, c = c , then

b² - 4ac > 0

1² - (4 × 1 × c) > 0

1 - 4c > 0 ( subtract 1 from both sides )

- 4c > - 1

Divide both sides by - 4, reversing the inequality as a result of dividing by a negative quantity.

c < $\frac{1}{4}$