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September 20, 2014

September 20, 2014

Posted by **Kristen** on Monday, February 4, 2013 at 9:21pm.

1. Use the discriminant to determine whether the given equation has two irrational roots, two rational roots, one repeated root, or two complex roots.

x^2-4x=5

a.) Two rational roots

b.) one repreated root

c.) two complex roots

d.) two irrational roots.

2.Use the discriminant to determine whether the given equation has two irrational roots, two rational roots, one repeated root, or two complex roots.

-3x^3+19x-20=0

a.) Two rational roots

b.) one repreated root

c.) two complex roots

d.) two irrational roots.

3. Use the discriminant to determine whether the given equation has two irrational roots, two rational roots, one repeated root, or two complex roots.

-5x^2-7x-5=0

a.) Two rational roots

b.) one repreated root

c.) two complex roots

d.) two irrational roots.

4. Use the discriminant to determine whether the given equation has two irrational roots, two rational roots, one repeated root, or two complex roots

x^2-12=7x

a.) Two rational roots

b.) one repreated root

c.) two complex roots

d.) two irrational roots.

- College Algebra -
**Reiny**, Monday, February 4, 2013 at 11:11pmAll these are based on the following concept (should be in your text)

for ax^2 + bx + c = 0

if b^2 - 4ac < 0 there are two imaginary or complex roots

if b^2 - 4ac = 0 , there is one root, (one repeated root)

if b^2 - 4ac > 0 , there are two distinct and real roots

if for the last case, b^2 - 4ac is a perfect square, then the two real roots will be rational, otherwise they are irrational.

in each case, evaluate b^2 - 4ac and decide where it fits in

remember to arrange the equation in the proper form

I will do #4

x^2 - 12 = 7x

x^2 - 7x - 12 = 0 , a=1, b=-7 , c= -12

b^2 - 4ac

= 49 - 4(1)(-12) = +97

so we will have 2 irrational roots

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