Prerequisites: Algebra Review

Self Check Quadratic Formula Self Check

Now, you try. Complete the self-check activity by looking at the questions below, working them out, and then clicking on the question to review the solution.

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Solve -g2 + 6g - 9 = 0 for g.

To solve this equation, use the quadratic equation.

Find the values of a, b, and c.
a equals negative 1, b equals six and c equals negative 9
Plug the values into the quadratic formula.
g equals opposite of six plus or minus the square root of six squared minus four times negative one times negative nine all over two times negative one
Use the plus sign in the formula and solve.
g equals negative six plus the square root of thirty six minus thirty six all over negative two, g equals negative six plus the square root of zero all over negative two,g equals negative six divided by negative two, g equals three
Use the minus sign in the formula and solve.
g equals negative six minus the square root of thirty six minus thirty six all over negative two, g equals negative six minus the square root of zero all over negative two, g equals negative six divided by negative two, g equals three

In this case, since the discriminate is equal to zero, g = 3 is the solution twice. In algebra, we call this a double root.

 

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Solve for 3p2 - 13p + 12 = 0 p.

Use the quadratic equation to solve this problem.

Find the values of a, b, and c.
a equals three, b equals negative thirteen and c equals twelve
Plug the values into the quadratic formula.
p equals opposite of negative thirteen plus or minus the square root of negative thirteen square minus 4 times three times twelve all over two times three
Use the plus sign in the formula and solve.
p equals thirteen plus the square root of one hundred sixty nine minus one hundred forty four all over six, p equals thirteen plus the square root of twenty five all over six, p equals thirteen plus five all over six, p equals eighteen divided by six, p equals three
Use the minus sign in the formula and solve.
p equals thirteen minus the square root of one hundred sixty nine minus one hundred forty four all over six, : p equals thirteen minus the square root of twenty five all over six, p equals thirteen minus five all over six, p equals eight divided by six, p equals four thirds,

The two solutions to this equation are p = 3 and p equals four thirds

 

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Solve 2x2 + 1 = 2x for x.

To solve for x first make sure it matches the standard form of the quadratic equation, then use the quadratic formula to solve.

Subtract 2x from both sides, rearrange into ax2 + bx + c = 0 format.
two times x squared plus one minus two x equals two x minus two x, two times x squared minus two x plus one equals zero
Find values for a, b, and c and plug into quadratic formula.
a equals two , b equals negative two, c equals one, x equals the opposite of negative two plus or minus the square root of negative two squared minus four times two times one all over two times one
Use the plus sign in the formula and solve.
x equals the opposite of negative two plus the square root of negative two squared minus four times two times one all over two times one, x equals two plus the square root of four minus eight all over two, x equals two plus the square root of negative four, x equals the quantity two plus two i end quantity divided by 2, x equals one plus i
Use the minus sign in the formula and solve.
x equals the opposite of negative two minus the square root of negative two squared minus four times two times one all over two times one, x equals two minus the square root of four minus eight all over two, x equals two minus the square root of negative four, x equals the quantity two minus two i end quantity divided by 2, x equals one minus i

In this case, we have imaginary roots!