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 ...

... 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 ...

... y = 5 3 5 3 12 5 Its determinant is ( ) − 4 × 1 × ( − ) > 0 . So it has two different real solutions. ... By the quadratic formula, the exact solutions are. ...

... D)E = ±√c/m Use the quadratic formula to solve ... Gauss-Jordan method to solve the system of equations. ... The determinant is ( −8) 2 − 4 × 1 × ( −3) = 76 ...

... 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 ...

... 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 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_ ...

... more details on assessing the quadratic model see ... The equation of motion for free transverse displacement w ... of natural frequencies and determinant derived from ...

...determinants of (firms') financial performance, Capon, Far- In addition ... we include lin- ear and quadratic time trends ... goodwill TABLE 2 defined in Equations 46 ...