Radicals and quadratics
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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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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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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, ...
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