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.
-$16 x ^ { 2 } + 8 x + 1 = 0$
A) Two distinct nonreal complex solutions
B) Two distinct rational solutions
C) Two distinct irrational solutions
D) One rational solution (a double solution)

Question

Quizplus · Accepted Answer

The discriminant of the quadratic equation $ax^2 + bx + c = 0$ is given by $b^2 - 4ac$. For the equation $16x^2 + 8x + 1 = 0$, $a = 16$, $b = 8$, and $c = 1$. The discriminant is $8^2 - 4 \times 16 \times 1 = 64 - 64 = 0$. A discriminant of 0 indicates one rational solution (a double solution).

Evaluate the Discriminant for the Equation 16x2+8x+1=016 x ^ { 2 } + 8 x + 1 = 016x2+8x+1=0

Evaluate the Discriminant for the Equation $16 x ^ { 2 } + 8 x + 1 = 0$