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Radicals and quadratics

Please see attachment.

Write the following expression in simplified radical form.

Find the roots of the quadratic equation:

Compute the value of the discriminant and give the number of real solutions to the quadratic equation

Solve the following equation for by using the quadratic formula:

Find the -intercept(s) and the coordinates of the vertex for the parabola . If there is more than one -intercept, separate them with commas.

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Hi,

Please find the solutions/explanations attached herewith.

1. Rewrite the following in simplified radical form.

Assume that all variables represent positive real numbers
Solution:

2. Write the following expression in simplified radical form.

Assume that all variables represent positive real numbers.
Solution:

3. Simplify the following expression as much as possible:

Assume that all variables represent positive real numbers.
Solution:

4.
Simplify.

Assume that all variables represent positive real numbers.
Solution:

5.
Multiply. Simplify your answer as much as possible.

Solution:

By combining similar terms, we will get

6.
Rationalize the denominator and simplify:

Solution:

7.
Write in simplified radical form by rationalizing the denominator.

Solution:

8.
Solve for :
,
where is a real number.
(If there is more than one solution, separate them with commas.)
Solution:
Squaring each side, we will get

z + 13 = 9
Subtract 13 from each side, we will get
z = 9 - 13 = -4
9.
Solve the following equation for :
,
where is a real number.
(If there is more than one solution, ...

Solution Summary

This provides several examples of working with radicals and quadratic equations, including graphing parabolas, simplifying, solving equations, and word problems.

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