Question

Geometry, Trigonometry, Logarithms, Coordinate Systems 1. a. State the standard form of a quadratic equation and its algebraic solution. b. Use this to find the solution(s) to -5t + 40t - 2 = 0.

Answer 1

a.

Standard form:

ax² + bx + c = 0

Solution:

`x = (-b \pm √(b^2 - 4ac))/(2a)`

b.
`t = 4 + (√(390))/(5)` or
`t = 4 - (√(390))/(5)`

Explanation:

a.

Standard form:

ax² + bx + c = 0

Solution:

`x = (-b \pm √(b^2 - 4ac))/(2a)`

b.

-5t² + 40t - 2 = 0

a = -5; b = 40; c = -2

`t = (-40 \pm √((40)^2 - 4(-5)(-2)))/(2(-5))`

`t = (-40 \pm √(1600 - 40))/(-10)`

`t = (40 \pm √(1560))/(10)`

`t = (40 \pm √(4 * 390))/(10)`

`t = (40 \pm 2√(390))/(10)`

`t = (20 \pm √(390))/(5)`

`t = 4 + (√(390))/(5)` or
`t = 4 - (√(390))/(5)`