Quadratic formulas..?

Question

The quadratic formula: Solve the quadratic equation by using the quadratic formula. If the
roots are irrational, give the rational approximations to the nearest tenth.

1. 3x^2 + 4x - 2 = 0
{___, ____}

2. x^2/3 + 1/2 = (5/6)x

{___,___}

Help, would be greatly appreciated!

Answer 1

1. 3x^2 + 4x - 2 = 0

Quadratic Form: x = [-b +/- V`b^2 - 4ac] / 2a

First: identify three terms...a = 3; b = 4; c = -2
Sec: replace the terms with the corresponding variables.

x = [-4 +/- V`4^2 - 4(3)(-2)] / 2(3)

x = [-4 +/- V`16 - 4(3)(-2)] / 6

x = [-4 +/- V`16 - 4(-6)] / 6

x = [-4 +/- V`16 + 24] / 6

x = [-4 +/- V`40] / 6

x = [-4 +/- V`2*2*2*5] / 6

x = [-4 +/- 2 V`10] / 6

Third: you will always have two solutions.

a. x = [- 4 + 2 V`10] / 6
x = - 4/6 + (2/6)V`10
x = - 2/3 + (V`10)/3

b. x = [- 4 - 2 V`10] / 6
x = - 4/6 - (2/6)V`10
x = - 2/3 + (V`10)/3

Answer 2

find the formula.

1) a = 3, the coefficient of x^2
b = 4, the coefficient of x
c = -2

now plug in these values to the formula. use calculator for approximation.

2) a = 1/3
b = -5/6 since must set equation equal to zero by subtracting (5/6)x from both sides. remember, quadratic equation must be equal to zero in order to use the quadratic formula.

c = 1/2

Answer 3

x=-4 +/- the square root of ((4)^2- 4(3)(2)) and all that divided by 2(3)

4+/- the square root of (16-24) divided by 6.
4+/- the square root of (-8) divided by 6
Therefore, the answer is no solution, because a negative number doesn't have a square root

Answer 4

1. [-4 +- sqrt(16+24)]/6
2. [(5/6)+-sqrt((25/36)-(4/6))]/(2/3)

Answer 5

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