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35 lines
1.4 KiB
Plaintext
35 lines
1.4 KiB
Plaintext
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; General quadratic (2nd degree polynomial) formula.
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; Formula for the 2 roots (solutions for x)
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; of the general quadratic equation.
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;
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a x^2 + b x + c = 0 ; The general quadratic equation.
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copy select ; Make a copy and select it.
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solve verifiable for x ; Mathomatic can easily solve and verify that:
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; This is the quadratic formula.
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; The coefficients (a, b, and c) may be any mathematical expression not containing x.
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pause
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; Here is the derivation and proof of the quadratic formula,
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; without actually using the quadratic formula,
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; because that is what we are trying to derive now, from the quadratic equation:
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#1:
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copy select ; make a copy of the general quadratic equation to work on and select it.
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-=c ; subtract "c" from both sides.
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/=a ; divide both sides by "a".
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pause Next simplify it and turn it into a repeated factor polynomial equation
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simplify
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+=b^2/(4*(a^2)) ; add "b^2/(4*(a^2))" to both sides.
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; Now the LHS is a repeated factor polynomial, next factor it by pressing Enter to simplify.
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pause
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simplify ; Now the LHS is a factored polynomial, so solving for the single "x" is easy.
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set debug 1 ; Let Mathomatic do the work and show it too.
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; Show how easy it is to solve this equation now, after pressing Enter.
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pause
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x
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; Here is the raw solve result, press the Enter key to simplify and compare with the quadratic formula.
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pause
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set no debug
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repeat simplify
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compare with 2
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