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High School Math : Solving Quadratic Equations

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Example Questions

Example Question #1 : Finding Roots

Find the zeros.

$f(t)=t^{2}-4t-21$

Possible Answers:

x=-7,3

x=7,-7

x=3,-3

x=-3,7

x=7,3

Correct answer:

x=-3,7

Explanation:

Factor the equation to (t-7)(t+3) . Set both equal to zero and you get and . Remember, the zeros of an equation are wherever the function crosses the -axis.

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Example Question #2 : Finding Roots

Find the zeros.

$f(x)=x^{2}-10x$

Possible Answers:

x=0

x=1,-1

x=10

x=0,10

x=-10

Correct answer:

x=0,10

Explanation:

Factor out an from the equation so that you have x(x-10) . Set and x-10 equal to . Your roots are and .

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Example Question #3 : Finding Roots

Find the zeros.

$f(x)=\frac{1}{5}(x+9)^{2}(x^{2}-4)$

Possible Answers:

x=-2,2

x=-9,-2,2

x=-9

x=2,-9

x=-3,3,-9

Correct answer:

x=-9,-2,2

Explanation:

Set (x+9)^2 equal to zero and you get . Set (x^2-4) equal to zero as well and you get and because when you take a square root, your answer will be positive and negative.

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Example Question #4 : Finding Roots

Find the zeros.

$f(x)=27x^{2}-45x-18$

Possible Answers:

$x=\frac{1}{3},2$

$x=\frac{1}{3}$

$x=-\frac{1}{3},2$

$x=9,-\frac{1}{3},2$

x=-2,-9

Correct answer:

$x=-\frac{1}{3},2$

Explanation:

Factor out a from the entire equation. After that, you get 9(3x^2-5x-2) . Factor the expression to (3x+1)(x-2) . Set both of those equal to zero and your answers are $-\frac{1}{3}$ and .

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Example Question #5 : Finding Roots

Find the zeros.

$f(x)=25x^{2}-81$

Possible Answers:

$x=\frac{9}{5}$

x=9,-9

$x=\frac{9}{5},-\frac{9}{5}$

x=5

$x=-\frac{9}{5}$

Correct answer:

$x=\frac{9}{5},-\frac{9}{5}$

Explanation:

This expression is the difference of perfect squares. Therefore, it factors to (5x-9)(5x+9) . Set both of those equal to zero and your answers are $\frac{9}{5}$ and $-\frac{9}{5}$ .

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Example Question #6 : Finding Roots

Find the zeros.

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

Possible Answers:

x=0

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

x=8

x=0,4

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

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 #7 : Finding Roots

Find the zeros.

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

Possible Answers:

x=-3,-2

x=-3,3

x=3,2

x=4,2

x=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 #1 : Solving Quadratic Equations

Find the zeros.

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

Possible Answers:

x=0

x=-6,6

x=6

x=0,6

x=1,-1

Correct answer:

x=0,6

Explanation:

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

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Example Question #2 : Solving Quadratic Equations

Find the zeros.

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

Possible Answers:

x=-2,4

x=2

x=4

x=2,-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 #3 : Solving Quadratic Equations

Find the zeros.

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

Possible Answers:

x=-5,8

x=0

x=-5

x=5,8

x=-8

Correct answer:

x=-5,8

Explanation:

Set both expressions to and you get and .

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High School Math : Solving Quadratic Equations

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #1 : Finding Roots

Example Question #2 : Finding Roots

Example Question #3 : Finding Roots

Example Question #4 : Finding Roots

Example Question #5 : Finding Roots

Example Question #6 : Finding Roots

Example Question #7 : Finding Roots

Example Question #1 : Solving Quadratic Equations

Example Question #2 : Solving Quadratic Equations

Example Question #3 : Solving Quadratic Equations

All High School Math Resources

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