Problem sET
Verbal
1. How do we recognize when an equation is quadratic?
2. When we solve a quadratic equation by factoring, why do we move all terms to one side, having zero on the other side?
3. In the quadratic formula, what is the name of the expression under the radical sign and how does it determine the number of and nature of our solutions?
Algebraic
For the following exercises, solve the quadratic equation by factoring.
4. [latex]{x}^{2}-9x+18=0[/latex]
5. [latex]6{x}^{2}+17x+5=0[/latex]
6. [latex]3{x}^{2}-75=0[/latex]
7. [latex]4{x}^{2}=9[/latex]
8. [latex]5{x}^{2}=5x+30[/latex]
9. [latex]7{x}^{2}+3x=0[/latex]
For the following exercises, determine the discriminant, and then state how many solutions there are and the nature of the solutions. Do not solve.
10. [latex]{x}^{2}+4x+7=0[/latex]
11. [latex]9{x}^{2}-30x+25=0[/latex]
12. [latex]6{x}^{2}-x-2=0[/latex]
For the following exercises, solve the quadratic equation by using the quadratic formula.
13. [latex]{x}^{2}+x=4[/latex]
14. [latex]3{x}^{2}-5x+1=0[/latex]
15. [latex]{x}^{2}=-25[/latex]
16. [latex]{x}^{2}+36=0[/latex]
17. [latex]{x}^{2}+2x+5=0[/latex]
18. [latex]{x}^{2}+8x+25=0[/latex]
19. [latex]{x}^{2}+6x+25=0[/latex]
20. [latex]{x}^{2}-6x+10=0[/latex]
21. [latex]x\left(x - 2\right)=10[/latex]
22. [latex]5{x}^{2}-8x+5=0[/latex]
23. [latex]2{x}^{2}-6x+5=0[/latex]
24. [latex]{x}^{2}-2x+4=0[/latex]