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High School Math : Algebra II

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8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #2 : Solving Quadratic Equations

Find the zeros.

f(x)= 36x^2-9x

Possible Answers:

x=0,4

x=8

$x=0,\frac{1}{4}$

x=0

$x=\frac{1}{4}$

Correct answer:

$x=0,\frac{1}{4}$

Explanation:

Factor the equation to 9x(4x-1) . Set both equal to and you get and $\frac{1}{4}$ .

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Example Question #1 : Solving Quadratic Equations

Find the zeros.

$f(x)=\frac{1}{4}x^2 +\frac{5}{4}x+\frac{3}{2}$

Possible Answers:

x=-3,3

x=3,2

x=-3,-2

x=2

x=4,2

Correct answer:

x=-3,-2

Explanation:

Factor a $\frac{1}{4}$ out of the quation to get

$\frac{1}{4}\left ( x^{2}+5x+6 \right )$

which can be further factored to

$\frac{1}{4}(x+3)(x+2)$ .

Set the last two expressions equal to zero and you get and .

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Example Question #5 : Solving Quadratic Equations

Find the zeros.

f(x)=x(x-6)^2

Possible Answers:

x=0

x=1,-1

x=-6,6

x=0,6

x=6

Correct answer:

x=0,6

Explanation:

Set each expression equal to zero and you get 0 and 6.

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Example Question #1 : Finding Roots

Find the zeros.

f(x)=(x-2)(x+4)^3

Possible Answers:

x=-2,4

x=2

x=2,-4

x=4

x=0,2,-2

Correct answer:

x=2,-4

Explanation:

Set both expressions equal to . The first factor yields . The second factor gives you .

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Example Question #2 : Finding Roots

Find the zeros.

f(x)=(x+5)(x-8)^2

Possible Answers:

x=-5

x=-5,8

x=5,8

x=-8

x=0

Correct answer:

x=-5,8

Explanation:

Set both expressions to and you get and .

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Example Question #11 : Finding Roots

Solve the following equation by factoring.

x^2+7x-8=0

Possible Answers:

$x=-8\ or\ 1$

$x=8\ or\ -1$

$x=-8\ or\ -1$

$x=8\ or\ 1$

Correct answer:

$x=-8\ or\ 1$

Explanation:

We can factor by determining the terms that will multiply to –8 and add to +7.

$8*-1=-8\ and\ 8+(-1)=7$

Our factors are +8 and –1.

0=x^2+7x-8=(x+8)(x-1)

Now we can set each factor equal to zero and solve for the root.

$x+8=0\ or\ x-1=0$

$x=-8\ or\ x=1$

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Example Question #12 : Finding Roots

Solve the following equation by factoring.

2x^2-8x-10=0

Possible Answers:

$x=-5\ or\ -1$

$x=5\ or\ 1$

$x=5\ or\ -1$

$x=-5\ or\ 1$

Correct answer:

$x=5\ or\ -1$

Explanation:

We know that one term has a coefficient of 2 and that our factors must multiply to –10.

$2*-5=-10\ and\ 2+2(-5)=-8$

Our factors are +2 and –5.

0=2x^2-8x-10=(2x+2)(x-5)

Now we can set each factor equal to zero and solve for the root.

$2x+2=0\ or\ x-5=0$

$x=-1\ or\ 5$

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Example Question #13 : Finding Roots

Solve the following equation by factoring.

0=x^3+4x^2+4x

Possible Answers:

$x=0\ or\ 2$

$x=0\ or\ -2$

$x= 0,2\ or\ -2$

$x=0,-4\ or\ 1$

Correct answer:

$x=0\ or\ -2$

Explanation:

First, we can factor an term out of all of the values.

0=x^3+4x^2+4x=x(x^2+4x+4)

We can factor remaining polynomial by determining the terms that will multiply to +4 and add to +4.

$2*2=4\ and\ 2+2=4$

Our factors are +2 and +2.

0=x(x+2)(x+2)=x(x+2)^2

Now we can set each factor equal to zero and solve for the root.

$x=0\ or\ (x+2)^2=0$

$x=0\ or\ -2$

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Example Question #311 : Algebra Ii

Solve $x^{2}+6x+5=0$

Possible Answers:

$x=-5\; or\; x=-2$

$x=-5\; or\; x=-1$

$x=3\; or\; x=-1$

$x=-3\; or\; x=-2$

$x=2\; or\; x=3$

Correct answer:

$x=-5\; or\; x=-1$

Explanation:

Factor the problem and set each factor equal to zero.

$x^{2}+6x+5=0$ becomes (x+5)(x+1)=0 so $x=-5 \; or\; x=-1$

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Example Question #15 : Finding Roots

Solve $x^{2}-8x+12=0$ .

Possible Answers:

$x=6\; or\; x=-8$

$x=-2\; or\; x=2$

$x=6\; or\; x=-8$

$x=-2\; or\; x=2$

$x=6\; or\; x=2$

$x=6\; or\; x=-4$

$x=-4\; or\; x=-2$

Correct answer:

$x=6\; or\; x=2$

Explanation:

Factor the quadratic equation and set each factor equal to zero:

$x^{2}-8x+12=0$ becomes (x-6)(x-2)=0 so the correct answer is $x=6\; or \; x=2$ .

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All High School Math Resources

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High School Math : Algebra II

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #2 : Solving Quadratic Equations

Example Question #1 : Solving Quadratic Equations

Example Question #5 : Solving Quadratic Equations

Example Question #1 : Finding Roots

Example Question #2 : Finding Roots

Example Question #11 : Finding Roots

Example Question #12 : Finding Roots

Example Question #13 : Finding Roots

Example Question #311 : Algebra Ii

Example Question #15 : Finding Roots

All High School Math Resources

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