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Transcript
Interpret the Discriminant (10.7)
To Solve Quadratic Equations in the form ax2 + bx + c = 0, where b  0 we can use the
Quadratic Formula:
 b  b  4ac 
2a
2
x
**Note: Be sure to put the equation
in standard form first:
ax2 + bx + c = 0
The b2 – (4ac) is called the discriminant
The value of the discriminant can be used to determine the number of solutions
We learned that a quadratic equation can have a different number of solutions:
2 Solutions
2 points of intersection
1 Solution
1 point of intersection
No Solution
No point of intersection
b2 – (4ac) is
Positive Number
b2 – (4ac) is
0
b2 – (4ac) is
Negative Number
1
Tell whether the equation has two solutions, one solution, or no solution.
Ex. 2x2 + 6x + 5 = 0
a = _____
b = _____
c = _____
b2 – (4ac) = _______________________ = ______
number of solutions: __________________
Ex. x2 + 4x + 3 = 0
a = _____
b = _____
c = _____
b2 – (4ac) = _______________________ = ______
number of solutions: __________________
Ex. 4x2 – 12x + 9 = 0
a = _____
b = _____
c = _____
b2 – (4ac) = _______________________ = ______
number of solutions: __________________
Ex. 3x2 – 7 = 2x
a = _____
b = _____
c = _____
b2 – (4ac) = _______________________ = ______
number of solutions: __________________
2