1c Review - Quadratics and complex roots

Decide how many and the type of solutions the quadratic has by finding the discriminant.

4x² - 8x + 6 = 0

• 2, real

• 2, imaginary

• 1 real

• 1 imaginary

Answer explanation

discriminant is -32. Since it is negative that means you will have 2 imaginary solutions.

Tags

CCSS.HSA.REI.B.4

Decide how many and the type of solutions the quadratic has by finding the discriminant.

x² - 6x + 9 = 0

• 2 real solutions

• 2 imaginary solutions

• 1 real solution

• 1 imaginary solution

Answer explanation

There is 1 real solution since the discriminant = 0.

Tags

CCSS.HSA.REI.B.4

Solve the following equation, select all solution(s).

(x-4)(3x+7)=0

• $-4$
  

• $\frac{-7}{3}$

• $3x^2-5x-28=0$

• 4

Answer explanation

The original problem is already factored, all you have to do is set them equal to 0 and solve. DO NOT do the "box" method.

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.REI.B.4

Solve the equation and find the solutions. List your answers as #,# with NO spaces and do not put "x = ". For a fraction use the / symbol.   $12x^2+30x$  

Answer explanation

you should have 2 answers since your GCF has an "x" in it - that automatically = 0. You are left with (2x+5) as a factor so your answer is -5/2 or

 $\frac{-5}{2}$  

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.REI.B.4

 $Find\ the\ solutions\ to\ 2x^2-4x+11=0.$  

•  $1\pm\sqrt{6}$  

•  $1\pm2i$  

•  $3,-1$  

•  $6,-2$  

Answer explanation

Remember the denominator is 2(a) so your denominator should have been 4. Also, when you have a negative square root that means "i" is in you answer.  Another common mistake is make sure you did $\left(-4\right)^2$ with ( ).  If you got  $\frac{4\pm8i^{ }}{4}$  you just forgot to simplify. 

Tags

CCSS.HSA.REI.B.4

Solve the following quadratic. Use whichever method(s) you find easiest (that will work)  $2x^2+2x-40=0$  

•  $8,\ -10$  

•  $-4,\ 5$  

•  $-8,\ 10$  

•  $-5,\ 4$  

Answer explanation

Remember your "a" value is 2 so if you factored without finding the gcf (2) first than you need to put (2x    )(2x     ). 

Tags

CCSS.HSA.REI.B.4

Solve the following quadratic.  $x^2-11x-31=-12$  

•  $\frac{11\pm\sqrt{51}}{2}$  

•  $\frac{11\pm\sqrt{197}}{2}$  

• 11 $\frac{11\pm\sqrt{293}}{2}$  

•  $\frac{11\pm3\sqrt{5}}{2}$ 

Answer explanation

Make sure you:
ADD 12 to both sides to get equation = 0
 put -11 in (   ) for when you square it, should = 121. 
Your "C" value is - 19

Tags

CCSS.HSA-REI.B.4B