MATH SOLVE

2 months ago

Q:
# A quadratic equation is shown below: 10x2 − 3x − 1 = 0 Part A: Describe the solution(s) to the equation by just determining the radicand. Show your work. (5 points) Part B: Solve 16x2 − 2x − 5 = 0 by using an appropriate method. Show the steps of your work, and explain why you chose the method used. (5 points)

Accepted Solution

A:

Part A:

For this case we have the following equation:

10x2 - 3x - 1 = 0

The radicand of the equation is:

root (b ^ 2 - 4 * a * c)

Substituting values:

root ((- 3) ^ 2 - 4 * (10) * (- 1))

root (9 + 40)

root (49)

49> 0

Therefore, the function has two real roots.

Part B:

For this case we have the following equation:

16x2 - 2x - 5 = 0

Factoring we have:

(2x + 1) * (8x-5) = 0

The solutions are:

x = -1/2

x = 5/8

The method of factoring is usually faster when solving quadratic equations.

For this case we have the following equation:

10x2 - 3x - 1 = 0

The radicand of the equation is:

root (b ^ 2 - 4 * a * c)

Substituting values:

root ((- 3) ^ 2 - 4 * (10) * (- 1))

root (9 + 40)

root (49)

49> 0

Therefore, the function has two real roots.

Part B:

For this case we have the following equation:

16x2 - 2x - 5 = 0

Factoring we have:

(2x + 1) * (8x-5) = 0

The solutions are:

x = -1/2

x = 5/8

The method of factoring is usually faster when solving quadratic equations.