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QUADRATIC EQUATIONS, image, image - Coggle Diagram
QUADRATIC EQUATIONS
Do you see b2 − 4ac in the formula above? It is called the Discriminant, because it can "discriminate" between the possible types of answer:
when b2 − 4ac is positive, we get two Real solutions
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Example:
If 3 2b 4 (a 1)x x (a b)x a.b 0 is a quadratic equation, find a and b.
a-1=0
a=1
2b-4=2
2b=2+4
2b=6
b=3
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Example:
Solve x2 − 4x + 6,25 = 0
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Note that the Discriminant is negative:
b2 − 4ac = (−4)2 − 4×1×6,25=-9
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BUT an upside-down mirror image of our equation does cross the x-axis at 2 ± 1,5 (note: missing the i).
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For a, b, c R and a 0 z , the expressions in the form of 2 ax bx c 0 are called quadratic
equations with variable x where the real numbers a, b, c are called coefficients
The values of x (they can be real or nonreal) which satisfy the given equation are called the roats of the equation and the set containing the roots is called solution set.
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