Using the Quadratic Formula

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Math › Using the Quadratic Formula

Questions 1 - 5

1

Solve using the quadratic formula:

$a=\frac{5 \pm i\sqrt{7}}{4}$

$a=\frac{6 \pm i\sqrt{7}}{4}$

$a=\frac{4 \pm i\sqrt{7}}{4}$

$a=\frac{3 \pm i\sqrt{7}}{4}$

$a=\frac{7 \pm i\sqrt{7}}{4}$

Explanation

Use the quadratic formula to solve:

$x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$

$a = \frac{-(-5) \pm \sqrt{(-5)^2-4(2)(4)}}{2(2)}$

$a = \frac{5 \pm \sqrt{-7}}{4}$

$a = \frac{5 \pm i\sqrt{7}}{4}$

2

Solve using the quadratic formula:

$x= \frac{-1 \pm i\sqrt{5}}{2}$

$x= \frac{-1 \pm i\sqrt{5}}{3}$

$x= \frac{-2 \pm i\sqrt{5}}{2}$

$x= \frac{-2 \pm i\sqrt{5}}{3}$

$x= \frac{-3 \pm i\sqrt{5}}{2}$

Explanation

Use the quadratic formula to solve:

$x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$

$x = \frac{-(2) \pm \sqrt{(2)^2-4(2)(3)}}{2(2)}$

$x = \frac{-2 \pm \sqrt{-20}}{4}$

$x = \frac{-2 \pm 2i\sqrt{5}}{4}$

$x = \frac{-1 \pm i\sqrt{5}}{2}$

3

Solve using the quadratic formula:

$x=\frac{-b \pm \sqrt{b^2-12ab}}{2a}$

$x=\frac{b \pm \sqrt{b^2-12ab}}{2a}$

$x=\frac{-b \pm \sqrt{b^2-12ab}}{a}$

$x=\frac{b \pm \sqrt{b^2-12ab}}{a}$

$x=\frac{-b \pm \sqrt{b^2-8ab}}{2a}$

Explanation

Use the quadratic formula to solve:

$x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$

$x = \frac{-(b) \pm \sqrt{(b)^2-4(a)(3b)}}{2(a)}$

$x = \frac{-b \pm \sqrt{b^2-12ab}}{2a}$

4

Solve using the quadratric formula:

$x=\frac{-ac\sqrt{a^2c^2-4bc}}{2b}$

$x=\frac{ac\sqrt{a^2c^2-4bc}}{2b}$

$x=\frac{ac\sqrt{a^2c^2-4bc}}{b}$

$x=\frac{-ac\sqrt{a^2c^2-4bc}}{b}$

$x=\frac{-ac\sqrt{a^2c^2-2bc}}{2b}$

Explanation

Use the quadratic formula to solve:

$x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$

$x = \frac{-(ac) \pm \sqrt{(ac)^2-4(b)(c)}}{2(b)}$

$x = \frac{-ac \pm \sqrt{a^2c^2-4bc}}{2b}$

5

A baseball that is thrown in the air follows a trajectory of , where is the height of the ball in feet and is the time elapsed in seconds. How long does the ball stay in the air before it hits the ground?

Between 3 and 3.5 seconds

Between 3.5 and 4 seconds

Between 2.5 and 3 seconds

Between 2 and 2.5 seconds

Between 4 and 4.5 seconds

Explanation

To solve this, we look at the equation .

Setting the equation equal to 0 we get .

Once in this form, we can use the Quadratic Formula to solve for .

The quadratic formula says that if , then

$x= \frac{-b\pm\sqrt(b^2-4ac)}{2a}$ .

Plugging in our values:

$t= \frac{-12\pm\sqrt{(12^2-4(-4)(6)}}{2(-4)}=\frac{-12\pm \sqrt{240}}{-8}= \frac{12\pm15.5}{8}$

Therefore or and since we are looking only for positive values (because we can't have negative time), 3.4375 seconds is our answer.

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