# Quadratic Equations and Determinants

Determine whether the following equations real or complex solutions; justify your answer. Note: It is not necessary to find the solutions; just determine if they are real or complex and explain why.

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

2. Form a quadratic equation that passes through the x-axis at x = 3 and x = -5. (must be an equation, not an expression.)

3. 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.

4. Steve traveled 200 miles at a certain speed. Had he gone 10mph faster, the trip would have taken 1 hour less. Find the speed of his vehicle.

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#### Solution Preview

a) determinant is 8*8 - 4*4*7 = -48; solution is complex

b) determinant is 6*6 - 4*7.5*13*7.5 = -2889; solution is complex

c) determinant is 1*1 - 4*2*-1 = 9; solution is real

d) determinant is -2*-2 - 4*4/3*3/4 = 0; solution is real

e) determinant is 5*5 - 4*2*5 = -15; solution is complex

f) determinant is -4*-4 - 4*1*4 = 0; solution is real

g) ...

#### Solution Summary

The following shows how to use the determinant to find out if quadratic equations have real or complex solutions. Also includes a few word problems.