# Sample quiz on real and non-real roots Main home here.

1. The discriminant of a quadratic in the form $ax^2+bx+c$ is given by $\cdots$?
A: $b^2-4ac$
B: $b^2+4ac$
C: $2b-4ac$
D: $4ac-b^2$
2. Calculate the discriminant of the quadratic $x^2+4x-3$
A: $4$
B: $20$
C: $28$
D: $-4$
3. Which of the following quadratics has a discriminant equal to $100$?
A: $x^2-8x-9$
B: $x^2-8x+9$
C: $x^2-9x+8$
D: $x^2+9x-8$
4. How many roots does a quadratic $ax^2+bx+c$ have if $b^2-4ac=0$?
A: $2$ distinct real roots
B: $2$ complex conjugate roots
C: $1$ repeated real root
D: No roots at all
5. How many roots does a quadratic $ax^2+bx+c$ have if $b^2-4ac> 0$?
A: $2$ complex conjugate roots
B: $1$ repeated real root
C: $1$ complex and $1$ real root
D: $2$ distinct real roots
6. How many roots does a quadratic $ax^2+bx+c$ have if $b^2-4ac< 0$?
A: No real roots
B: $1$ repeated real root
C: $1$ real and $1$ complex root
D: $2$ distinct real roots
7. Determine the number of roots of the quadratic $y=x^2-4x+4$.
A: $3$
B: $2$
C: $1$
D: $0$
8. How many roots does the quadratic $y=2x^2-5x+3$ have?
A: $3$
B: $2$
C: $1$
D: $0$
9. How many roots does the quadratic $y=x^2+x+1$ have?
A: $3$
B: $2$
C: $1$
D: $0$
10. For what value(s) of $b$ will the quadratic $y=x^2+bx+16$ have equal roots?
A: $b=\pm 8$
B: $b=\pm 4$
C: $b=8$
D: $b=4$
11. For which of the following values of $b$ will the quadratic $y=2x^2+bx+9$ have $2$ distinct real roots?
A: $6$
B: $7$
C: $8$
D: $9$
12. Determine the roots of the quadratic $y=4x^2+4x+1$
A: $x=-\frac{1}{2}$
B: $x=-2$
C: $x=\frac{1}{2}$
D: No real root
13. Find the roots of the quadratic $y=x^2-49x+600$
A: $x=-24,-25$
B: $x=-20,-30$
C: $x=24,25$
D: $x=20,30$
14. For which of the following values of $c$ will the quadratic $2x^2+3x+c$ have no real roots?
A: $0$
B: $1$
C: $2$
D: $\frac{1}{2}$
15. For which of the following values of $a$ will the quadratic $y=ax^2+4x+1$ have $2$ distinct real roots?
A: $4$
B: $3$
C: $5$
D: $7$
16. Determine the roots of the quadratic $y=3x^2+4x+1$
A: $x=-1,-\frac{1}{3}$
B: $x=-1,-\frac{4}{3}$
C: $x=-1,-3$
D: $x=1,\frac{1}{3}$
17. Determine the roots of the quadratic $y=ax^2+2ax+a$
A: $x=-a$
B: $x=-\frac{1}{a}$
C: $x=-1$
D: $x=-2a$
18. Determine the roots of the quadratic $y=x^2-8x-9$
A: $x=-1,9$
B: $x=-9,1$
C: $x=-1,-9$
D: $x=-1,-8$
19. If $x=3$ is a root of the quadratic $y=x^2+bx-12$, determine the value of $b$.
A: $-1$
B: $-2$
C: $2$
D: $1$
20. If $x=5$ is a root of the quadratic $y=x^2+bx-15$, determine the other root.
A: $2$
B: $3$
C: $-2$
D: $-3$