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By Rational Root Theorem, all rational roots of a polynomial are in the form \frac{p}{q}, where p divides the constant term 96 and q divides the leading coefficient 1. List all candidates \frac{p}{q}.

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Find one such root by trying out all the integer values, starting from the smallest by absolute value. If no integer roots are found, try out fractions.
By Factor theorem, x-k is a factor of the polynomial for each root k. Divide x^{4}+14x^{3}+71x^{2}+154x+96 by x+1 to get x^{3}+13x^{2}+58x+96. Solve the equation where the result equals to 0.
By Rational Root Theorem, all rational roots of a polynomial are in the form \frac{p}{q}, where p divides the constant term 96 and q divides the leading coefficient 1. List all candidates \frac{p}{q}.

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Find one such root by trying out all the integer values, starting from the smallest by absolute value. If no integer roots are found, try out fractions.
By Factor theorem, x-k is a factor of the polynomial for each root k. Divide x^{3}+13x^{2}+58x+96 by x+6 to get x^{2}+7x+16. Solve the equation where the result equals to 0.

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All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Substitute 1 for a, 7 for b, and 16 for c in the quadratic formula.
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