SOLUTION: In questions 6-9, use the discriminant to determine the number of solutions of the quadratic equation, and whether the solutions are real or complex. Note: It is not necessary to

Question 585004: In questions 6-9, use the discriminant to determine the number of solutions of the quadratic equation, and whether the solutions are real or complex. Note: It is not necessary to find the roots; just determine the number and types of solutions.
The above is the instructions for the problems. Below I have worked out each math problem, but once again, I'm not sure whether or not the solutions I have are real or complex. I think I worked each problem out correctly. If I have not please let me know. If I have, I guess the only thing I need clarifying on is if the solution I have is real or complex.
6. x�+6x-7=0
Use the quadratic formula to find the solutions.
X=-b�√b�-4ac ax�+bx+c=0
2a
A=1, B=6, C=-7
b�-4ac The discriminant of a quadratic is the expression inside the radical of the quadratic formula.
((6)�-4(1)(-7)) Substitute in the values of a,b, and c.
36-4(1)(-7) Squared 6
36-4(-7) Multiplied 1 by -7
36+28 Multiplied -4 by each term inside the parenthesis.
64 Added 36+28
ANSWER: 64 Real or complex????

7.z�+z+1=0
Use the quadratic formula to find the solutions.
X=-b�√b�-4ac ax�+bx+c=0
2a
A=1, B=1, C=1
b�-4ac The discriminant formula
((1)�-4(1)(1)) Substitute in the values of a,b, and c
1-4(1)(1) Expand the exponent 2 to the expression
1-4(1) Multiply 1*1
1-4 Multiply -4 by each term inside the parenthesis
-3 Subtract 4 from 1
ANSWER: -3 Real or complex??

8. (3)�y�-4y-7(3)^�=0
√(3)*y�-4y-7(3)^�=0 An expression with a fractional exponent can be written as a radical with an index equal to the denominator of the exponent
√3*y�-4y-7(3)^�=0 Removed the parenthesis around the expression 3
√3*y�-4y+(-7*√(3))=0 Reduced
√3*y�-4y+(-7*√3)=0 Removed the parenthesis around the expression 3
√3*y�-4y+(7√3)=0 Multiplied -7 by √
y�√3-4y-7√3=0 Multiplied √3 by y�
Y=-b�√b�-4ac ay�+bx+c=0
2a
A=√3, B=-4, C=-7√3
b�-4ac Discriminant formula
((-4)�-4(√3)(-7√3)) Substitute in the values of a,b,c
(4)(-4)-4(√3)(-7√3) Squared
16-4(√3)(-7√3) Multiply to simplify the expression (-4)(-4)
16-4(-7√3�) Multiply -7W to get -7W�
16+28√3� Multiplied -4 by each term inside the parenthesis.
16+28(3) Squared
16+84 Multiplied 28 by each term inside the parenthesis.
ANSWER: 100 Real or complex???

9. 2x�-10x+25=0
X=-b�√b�-4ac ax�+bx+c=0
2a
A=2, B=-10, C=25
b�-4ac
((-10)�-4(2)(25)) Substitute in the values of a,b, and c.
(-10)(-10)-4(2)(25) Squared
100-4(2)(25) Multiplied to simplify the expression (-10)(-10)
100-4(50) Multiplied 2 by25
100-200 Multiplied -4 by each term inside the parenthesis.
ANSWER: -100 real or complex??

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
The quantity is the determinant. This determines whether your solutions are real or complex. If is positive, then you'll have two real solutions. In the first problem (#6), you found that . Since this is a positive number, this means that you have two real solutions.

On the other hand, for problem #9, you got -100. This means that there are 2 complex solutions.

Hope this clears things up a bit. If not, let me know.
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