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. x²+6x-7=0
Use the quadratic formula to find the solutions.
X=-b±√b²-4ac ax²+bx+c=0
2a
A=1, B=6, C=-7
b²-4ac The discriminant of a quadratic is the expression inside the radical of the quadratic formula.
((6)²-4(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.z²+z+1=0
Use the quadratic formula to find the solutions.
X=-b±√b²-4ac ax²+bx+c=0
2a
A=1, B=1, C=1
b²-4ac The discriminant formula
((1)²-4(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)½y²-4y-7(3)^½=0
√(3)*y²-4y-7(3)^½=0 An expression with a fractional exponent can be written as a radical with an index equal to the denominator of the exponent
√3*y²-4y-7(3)^½=0 Removed the parenthesis around the expression 3
√3*y²-4y+(-7*√(3))=0 Reduced
√3*y²-4y+(-7*√3)=0 Removed the parenthesis around the expression 3
√3*y²-4y+(7√3)=0 Multiplied -7 by √
y²√3-4y-7√3=0 Multiplied √3 by y²
Y=-b±√b²-4ac ay²+bx+c=0
2a
A=√3, B=-4, C=-7√3
b²-4ac Discriminant formula
((-4)²-4(√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√3²) Multiply -7W to get -7W²
16+28√3² 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. 2x²-10x+25=0
X=-b±√b²-4ac ax²+bx+c=0
2a
A=2, B=-10, C=25
b²-4ac
((-10)²-4(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):
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