For the following equation: 2x^2 -3x + 7 = 0 (1) Calculate the discriminant
(2) Determine the number and type of solutions
(3) Use the quadratic formula to solve

Part 1)

Part 2)

Since our discriminant is negative, we will have two complex (imaginary) solutions.

Part 3)

Step-by-step explanation:

We have the equation:

Labelling our coefficients, we see that:

Part 1)

The discriminant (symbolized as Δ) is given by the formula:

So, the value of our discriminant is:

Evaluate:

Part 2)

Remember the guidelines for the discriminant:

Since our discriminant is a negative value, we will have two complex (imaginary) roots.

Part C)

The quadratic formula is given by:

By substitution:

Evaluate:

Simplify the square root:

Therefore:

Hence, our two zeros are:

And in standard form:

the discriminant is b squared - 4 (a) (c) where a = 2, b = -3, and c = 7

after plugging in, the discrimimant is -47

if the discriminant is negative then it has no 'real' roots (the graph will not intersect the x-axis) but it has 2 solutions:  (3+47i)/2 and (3-47i)/2 where 47i equals the square root of negative 47

Step-by-step explanation:

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.

step-by-step explanation:   divide the numerator by the denominator to get the decimal

it would still be 193

if divide by 100 then 1.93

i am not sure