Use the discriminant to find what type of solutions (two rational, two irrational, one rational, or two nonreal complex)
each of the following equations has. Do not solve the equation.
-$$x ^ { 2 } + 3 x - 4 = 0$$
A) two irrational solutions
B) two nonreal complex solutions
C) one rational solution
D) two rational solutions

Question

Quizplus · Accepted Answer

The discriminant of a quadratic equation $ax^2 + bx + c = 0$ is given by $b^2 - 4ac$. For the equation $x^2 + 3x - 4 = 0$, the discriminant is $3^2 - 4(1)(-4) = 9 + 16 = 25$. Since 25 is a perfect square and positive, the equation has two rational solutions.

Use the Discriminant to Find What Type of Solutions (Two x2+3x−4=0x ^ { 2 } + 3 x - 4 = 0x2+3x−4=0

Use the Discriminant to Find What Type of Solutions (Two $x ^ { 2 } + 3 x - 4 = 0$