Quadratic Equations???

Question

For the first on, 5x^2 + 8x + 7=0, I was given an explanation of
B^2 - 4ac
8^2 - 4(5)(7)
= -76 since neg, zero answer
and
#6 or f this was explained: (-4)^2 -4(1)(4)=0 since zero, 1 solution
I am even more confused now. Can anyone explain in a easier form?
Ok, I know that having a solution means if you substitute with a # and the equation is still true, but this question is not giving me any #'s to plug in. Does anyone know what I am suppose to do? Thanks!

1. 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

Answer 1

The formula for solution of a quadratic equation of the form:
ax^2 + bx + c = 0
is:
x = ( -b +/- sqrt( b^2 - 4ac ) ) / 2a.

The quantity b^2 - 4ac which is under the square root sign is known as the discriminant.
When any positive or negative number is squared, the result is always positive.
If, therefore, b^2 - 4ac is negative, the equation has no roots.

If b^2 - 4ac = 0, then both of the roots simplify to:
-b / 2a .....(1),
showing that there is only one root.

Equation (f) p^2 - 4p + 4 = 0 has just one root, as you say. Its value, from the simpler formula (1) above is 4 / 2 = 2.

Answer 2

The equation of the parabola is ax^2 +bx +c = 0.

If b^2-4ac >0, there will be two real roots, because the parabola will intersect the x-axis in two places.
If b^2-4ac = 0, there will be one root because the parabola will be tangent to the x-axis an touch it at one point only.
If b^2-4ac <0 there will be no real roots because the parabola will never intersect the x-axis at all. The parabola will lie entirely above the x=axis or entirely below the x-axis. In this last case, the roots are imaginary.

Answer 3

Have you ever thought about doing your own homework for a change? You had the audacity to type in 11 questions that need answers...how about attending an extra help session instead...