Name Date
WORKSHEET 5.23: USING THE DISCRIMINANT
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The discriminant,b^2 − 4 ac, is the expression that is inside the radical symbol in the quadratic
formula,x=
−b±
√
b^2 − 4 ac
2 a
. The discriminant can be used to determine the number of
solutions of a quadratic equation expressed in standard form asax^2 +bx+c= 0 , where
a= 0. Use the guidelines below:
- Write the equation in standard form, if necessary.
- Identify the values ofa,b,andc.
- Substitute these values in the discriminant and use the order of operations to find the
value of the discriminant.- If the value of the discriminant is 0, the equation has one solution.
- If the value of the discriminant is positive, the equation has two solutions.
- If the value of the discriminant is negative, the equation has no real solutions.
Example 1 Example 2 Example 3
x^2 − 4 x+ 4 = 0 x^2 + 5 x+ 3 = 02 x^2 +x+ 5 = 0
a=1,b=−4,c= 4 a=1,b=5,c= 3 a=2,b=1,c= 5
(−4)^2 −4(1)(4) 52 −4(1)(3) 12 −4(2)(5)
16 − 625 − 12 1 − 40
013 − 39
There is one solution. There are two solutions. There are no real solutions.
DIRECTIONS: Use the discriminant to determine the number of solutions. If there are no
real solutions, write ‘‘no real solutions.’’
- x^2 + 6 x− 5 = 0 2. x^2 − 4 x+ 10 = 0
- x^2 − 2 x− 3 = 0 4. x^2 + 6 x=− 9
CHALLENGE:Why is finding the discriminant an important step to take before
solving an equation?
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Copyright
©
2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.