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QUADRATIC EQUATIONS - Coggle Diagram
QUADRATIC EQUATIONS
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KEY WORDS
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Solution Set: A solution set is the set of all variables that makes the equation true. For example, the solution set to x² = - 9 is Ø, because no number, when squared, is equal to a negative number. Sometimes we will be given a set of values from which to find a solution -a replacement set.
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Complex Number:In relation to quadratic equations, imaginary numbers (and complex numbers) occur when the value under the radical portion of the quadratic formula is negative. When this occurs, the equation has no roots (zeros) in the set of real numbers.
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For a,b,c ∈ R and a ≠ 0, the solution set of the equation ax²+bx+c=0 is found by factoring out by using common factor if c=0 in the given equation.
EXPRESSION OF A COMPLEX NUMBER IN FORM OF a+bi (a,b ∈ R)
A complex number is the sum of a real number and an imaginary number. A complex number is expressed in standard form when written a + bi where a is the real part and bi is the imaginary part. For example, 5+2i 5 + 2 i is a complex number.
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If a quadratic equation with real coefficients has a negative discriminant (△﹤0), the two solutions of the equation are complex conjugates of each other. If one of the roots of a quatratic equation is a+bi then the other one is a-bi.
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