Determine the type and number of solutions of -4x^2 - 3x + 7 = 0?

Answer 1

first you need to break the function up into two parts:
(4x+7)(-x+1) - if you multiply this back out you can see that it equals the orignal equation.

then set both parts equal to 0 and solve:
4x+7=0 OR -x+1=0
4x=-7 OR 1=x

x = (-7/4) or 1

Answer 2

Think of the equation as in ax^2 + bx + c = 0 form.
a = -4 b = -3 c = 7

You have to use the discriminant, b^2 - 4ac, to find the type and number of solutions. The discriminant is derived from the quadratic formula,
x = [-b +/- √(b^2 - 4ac)] / (2a).

The discriminant is the part under the square root. If it is zero, there is one real solution, since the square root of zero is zero and +/- 0 is always zero. If the discriminant is positive, there are two real solutions, since the square root of a positive is real, and nonzero (thereby affected by +/- and giving two answers). However, if the discriminant is negative, there are two complex solutions, since the square root of a negative is complex (and affected by +/-).

So in your equation, b^2 - 4ac = (-3)^2 - 4(-4)(7) = 9 + 112 = 121. Hence, you have two real solutions.

As a bonus, you know know that your answers are rational, because 121 is a perfect square!

Answer 3

There is only one solution because the maximum number of relative extrema is the power function minus 1. 2-1=1. Therefore the highest number of solutions is 1.

As for the answer, factor it out and you should get the answer.

Answer 4

4x² + 3x - 7 = 0
x = [- 3 ± √37 ] / 8
x = (- 3 + √37) / 8 , x = (- 3 - √37) / 8
Two solutions
Solutions are irrational numbers.

Answer 5

Type: real numbers

Number of solution: 2, because it is quadratic