Evaluate the discriminant for the equation. Then use it to predict the number of distinct solutions, and whether they are rational, irrational, or nonreal complex.
-$25 x ^ { 2 } - 10 x + 1 = 0$
A) Two distinct rational solutions
B) Two distinct nonreal complex solutions
C) One rational solution (a double solution)
D) Two distinct irrational solutions

Question

Quizplus · Accepted Answer

The discriminant of the quadratic equation $ax^2 + bx + c = 0$ is given by $b^2 - 4ac$. For the equation $25x^2 - 10x + 1 = 0$, $a = 25$, $b = -10$, and $c = 1$. The discriminant is $(-10)^2 - 4(25)(1) = 100 - 100 = 0$. A discriminant of 0 indicates one rational solution (a double solution).

Evaluate the Discriminant for the Equation 25x2−10x+1=025 x ^ { 2 } - 10 x + 1 = 025x2−10x+1=0

Evaluate the Discriminant for the Equation $25 x ^ { 2 } - 10 x + 1 = 0$