Advanced Math practice question

Answer: A. Zero

The number of real solutions of ax² + bx + c = 0 depends on the discriminant b² − 4ac. Here it is 3² − 4(2)(5) = 9 − 40 = −31. A negative discriminant means the square root in the quadratic formula is of a negative number, so there are no real solutions.

Why the other answers are wrong

B. Exactly one

Exactly one real solution happens only when the discriminant is exactly 0. Here it's −31.

C. Exactly two

Two real solutions need a positive discriminant. 9 − 40 is negative, so the parabola never reaches the x-axis.

D. Infinitely many

A quadratic equation can never have infinitely many solutions — at most two. That would require every term to be zero.

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