Transcription of Solving Cubic Polynomials - SHSU
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Solving Cubic Polynomials - SHSU
Solving Cubic The general solution to the quadratic equationThere are four steps to finding the zeroes of a quadratic First divide by the leading term, making the Then, givenx2+a1x+a0, substitutex=y a12to obtain an equation without the linear term.(This is the depressed equation.)3. Solve then foryas a square root. (Remember to use both signs of the square root.)4. Once this is done, recoverxusing the fact thatx=y example, let s solve2x2+ 7x 15 = , we divide both sides by 2 to create an equation with leading term equal to one:x2+72x 152= replacexbyx=y a12=y 74to obtain:y2=16916 Solve fory:y=134or 134 Then, Solving back forx, we havex=32or method is equivalent to completing the square and is the steps taken in developing the much-memorized quadratic formula.
q is a rational solution to the polynomial equation f(x) = 0 then qx pis a factor of the polynomial f(x) and so we can use long division to write f(x) = (qx p)g(x) where g(x) is a polynomial of smaller degree. We teach a version of this method in high school when students learn to solve quadratic equations by factoring.
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