Equations
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Determine whether the following equations have a solution or not? Justify your answer.
a) 5x2 + 8x + 7 = 0
b) (7)1/2y2 - 6y - 13(7)1/2 = 0
c) 2x2 + x - 1 = 0
d) 4/3x2 - 2x + 3/4 = 0
e) 2x2 + 5x + 5 = 0
f) p2 - 4p + 4 = 0
g) m2 + m + 1 = 0
h) 3z2 + z - 1 = 0
If x = 3 and x = -5, then form a quadratic equation.
What type of solution do you get for quadratic equations where D < 0? Give reasons for your answer. Also provide an example of such a quadratic equation and find the solution of the equation.
Create a real-life situation that fits into the equation (x + 3)(x - 4) = 0 and express the situation as the same equation.
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a) 5x2 + 8x + 7 = 0
D = b^2 - 4ac
= 64 - 140
= -76
Since D = -76 less than 0 no real solution exists.
b) (7)1/2y2 - 6y - 13(7)1/2 = 0
D = 36 + 364
= 400
Since D = 400 which is greater than 0 there are real solutions.
c) 2x2 + x - 1 = 0
D = 1 + 8
= 9
Since D = 9 which is greater than 0 there are real solutions.
d) 4/3x2 - 2x + 3/4 = 0
D = 4 - 4
= 0
Since D = 0, there is one solution.
e) 2x2 + 5x + 5 = 0
D = 25 - ...
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