This expression is called the Discriminant, also shown as Δ.
It is equal to b² - 4ac. This is a very important part of the quadratic formula as it determines whether x will have two values, one repeated value or no real values. Here are a few examples.
a) x² - 2x - 1. a is equal to 1 since 1x² = x². b = -2, c = -1
The discriminant will be (-2)² - 4×1×-1 = 4 + 4 = 8.
Since Δ > 0, there are two x values. Graphed, the parabola sinks below the x axis.
b) x². a = 1, b = 0 (0x = 0), c = 0
The discriminant will be 0² - 4×1×0 = 0 - 0 = 0.
Since Δ = 0, there is only one x value. Graphed, the parabola touches the x axis at only one point.
c) x² + 1. a = 1, c = 1.
The discriminant will be 0² - 4×1×1 = 0 - 4 = -4
Since Δ < 0, there are no real x values. Graphed, the parabola floats above the x axis.
Hope this helps!
( - 45, 0)
to find the x-intercept let y = 0 in the equation
x = 0 → 
x = - 15
multiply both sides by 3
x = 3 × - 15 = - 45
x-intercept = ( - 45, 0)
0.05n + 0.25q = 1.60
q = 3n
0.05n + 0.25(3n) = 160
0.05n + 0.75n = 1.60...multiply by 100 to get rid of the decimals
5n + 75n = 160...answer D
M=6/5 and n = sqrt(2), is rational (but not an integer) and n is irrational.
The case with n = sqrt(9)=3, is not a solution. The case with m=4pi neither.
The last case is m = 6/2=3, integer, so neither works.
So, it is the one with m=6/5 and sqrt(2)
