3.04 Quadratic formula
Considering the quadratic formula, find the values of a, b and c in the following quadratic equations:
Solve the following equations using the quadratic formula:
x^{2} + 5 x + 6 = 0
x^{2} - 5 x + 6 = 0
x^{2} - 5 x + \dfrac{9}{4} = 0
x^{2} - 8 x + \dfrac{55}{4} = 0
4 x^{2} + 7 x + 3 = 0
4 x^{2} - 17 x - 15 = 0
- 6 + 7 x + 5 x^{2} = 0
- 6 - 13 x + 5 x^{2} = 0
- 20 - 11 x + 3 x^{2} = 0
- 20 + 21 x + 5 x^{2} = 0
Solve the following equations, leaving your answer in surd form:
x^{2} - 7 x + 9 = 0
x^{2} - 5 x - 2 = 0
- 2 x^{2} - 15 x - 4 = 0
5 x^{2} - 15 x + 2 = 0
- 5 x^{2} - 15 x + 3 = 0
5 x = \left(x - 5\right) \left( 3 x + 3\right)
\dfrac{3 x + 1}{3 x - 1} - \dfrac{3 x - 1}{3 x + 1} = 5
Consider the equation 2 x^{2} = 14 .
Solve for x using the quadratic equation. Give your answer in surd form.
Give x as decimal number correct to three decimal places.
Solve the following equations, rounding your answers to three decimal places:
x^{2} + 3 x - 6 = 0
x^{2} + 7 x - 3 = 0
4 x^{2} + 7 x + 2 = 0
5 x^{2} + 9 x + 2 = 0
2 x \left(x - 4\right) = 3 x + 1
3 x \left(x + 4\right) = - 3 x + 4
7.1 x^{2} + 5.3 x - 1.5 = 0
1.8 x^{2} + 5.2 x - 2.3 = 0
Solve the following expression for m: 10 - 6 m + 2 m^{2} = m^{2} + 8 m + 9
For each of the given solutions to a quadratic equation:
Find the values of a, b and c.
Write down the quadratic equation that has these solutions.
An object is launched from a height of 80 \text{ ft} with an initial velocity of 107 \text{ ft/s}.
After x seconds, its height, h, is given by:
h = - 16 x^{2} + 107 x + 80
Find the number of seconds, x, after which the object is 30 \text{ ft} above the ground. Round your answer to one decimal place.
An object is launched from a height of 8 \text{ m} with an initial velocity of k \text{ ms}^{-1}.
After t seconds, its height, h(t), is given by:
h(t) = -2 t^{2} + k t + 8
The object was in flight for 4 seconds before reaching the ground. What was its initial velocity k ?