QUADRATIC EQUATIONS WORKSHEET

Solve each equation by the two methods written in parentheses. Write, in complete
sentences, which method you preferred in each problem and why. Show your work
in the space provided.

1. 2x²- X - 15 = 0 ( Factoring and the quadratic formula)

2. (x - 9)²= - 25 ( Square root property and the quadratic formula)

3. x²+ 18x = - 57 (Completing the square and the quadratic formula )

4. 5x²= 12x (Factoring and the quadratic fonnula)

5. 8x²- 12x + 3 = 0 (Solve by any method you choose and write an explanation as to
why you chose that method.)

De termining the Nature of the Roots by Finding the Discriminant

The discriminant of the quadratic formula is the part of the formula that is underneath
 the square root, b²- 4ac.

Since this value occurs underneath a square root, the value of the discriminant actually
determines the nature of the roots of the equation. .

If b²- 4ac > 0, then the quadratic equation has two real roots because you are taking
the square root of a positive number which is real.

If b²- 4ac < 0, then the quadratic equation has two complex roots because you are
taking the square root of a negative number which is imaginary.

If b²- 4ac =0, then the quadratic equation has one real, repeated root because you are
taking the square root of a zero, so when you calculate ± 0, you get the same value for both roots.

Examples: Determine the nature of the roots for each quadratic equation by finding
the value of its discriminant.

I)  x²+ 4 = 4x
2) x²+ 2x + 6 = 0
3) x²= 9

Solutions:

NOW TRY THESE

Directions: For each equation, calculate the discriminant and then state the nature of the roots.

Compare these solutions to those you got when graphing the equations . They should be the same.

NOW TRY THESE

Directions: Use the quadratice formula to solve each of the equations in #1 -#9 above, and then
write the solution set.