Sample quiz on real and non-real roots
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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: $-3$