1.03 Solve using the quadratic formula
Is the following statement true or false?
'Any quadratic equation that can be solved by completing the square can also be solved by the quadratic formula.'
The standard form of a quadratic equation is a x^{2} + b x + c = 0. Find the values of a, b and c in the quadratic equations below:
x^{2} + 7 x + 10 = 0
4 x^{2} + 3 x = 5
3 x^{2} - 8 x + 2 = 9 x - 7
Solve the following equations using the quadratic formula:
x^{2} + 11 x + 28 = 0
x^{2} - 5 x + 6 = 0
4 x^{2} - 7 x - 15 = 0
x^{2} + 5 x + \dfrac{9}{4} = 0
- 6 - 13 x + 5 x^{2} = 0
Solve the following equations using the quadratic formula. Leave your answers in surd form.
x^{2} - 5 x - 2 = 0
4 x^{2} - x - 10 = 0
- 2 x^{2} - 15 x - 4 = 0
Solve the following equations using the quadratic formula. Round your answers to 1 decimal place.
1.8 x^{2} + 5.2 x - 2.3 = 0
x^{2} + 7 x - 3 = 0
3 x \left(x + 4\right) = - 3 x + 4
Consider the equation x \left(x + 9\right) = - 20.
Solve it by the method of factorisation.
Check your solution by solving it using the quadratic formula.
Using the quadratic formula, the solutions to a quadratic equation of the form
ax^2 + bx + c = 0 are given by: x = \dfrac{- 5 \pm \sqrt{5^{2} - 4 \times \left( - 7 \right) \times 10}}{2 \times \left( - 7 \right)}
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 90 feet with an initial velocity of 131 feet per second. After x seconds, its height (in feet) is given by h = - 16 x^{2} + 131 x + 90
Solve for the number of seconds, x, after which the object is 20 feet above the ground. Give your answer to the nearest tenth of a second.