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.

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.

... The quadratic formula always work. For problem 1, x^2+6x+8=0 a=1, b=6, c=8 determinant: b^2-4ac=6^2-4*1*8=4 solutions: (-b±sqrt(b^2-4ac))/2a=(-6±sqrt(4))/(2*1 ...

... signs of the leading coefficients in front of these smaller determinants. ... In a system, if one equation is linear and the other is quadratic, then the ...

... x+y=5 xy=1. iv) Using determinants solve the following equations : a) 2x+y = 3 x+y = -2. ... i) Solve he following equation by the quadratic formula : ...

... Evaluate the determinant 11. Evaluate the expression 12. ... The graphs in Fig. 39 show that a system of equations consisting of a quadratic equation and a ...

... variable in the study of the " Determinants of the ... of all other independent variables in the equation. ... a. linear b. quadratic c. multiplicative d. hyperbolic e ...

... The quadratic equation with roots -1 and -5 is. Therefore the sought-for differential equation is ... since the matrix is inverible (indeed, its determinant is not ...

... the equation manipulation and works as long as the determinant of the ... In a system, if one equation is linear and the other is quadratic, then the ...

... detailed steps for how this can be a normal quadratic matrix as ... U}}(1,0,0)={pmatrix} 0&1 1&0 {pmatrix}, {equation} which has determinant -1. Therefore F_ ...

... by 3 symmetric matrices A produce following functions f = X ... logic is that the second matrix has zero determinant. ... coefficients in front of the quadratic form we ...