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Popular >

solvefor x,0=x^4-12x^3-42x^2+11

Solution

solve for

x, 0 = x^{4} - 12 x^{3} - 42 x^{2} + 11

Solution

x \approx - 0.56098 \dots, x \approx 0.48101 \dots, x \approx - 2.74896 \dots, x \approx 14.82892 \dots

Solution steps

0 = x^{4} - 12 x^{3} - 42 x^{2} + 11

Switch sides

x^{4} - 12 x^{3} - 42 x^{2} + 11 = 0

Find one solution for

x^{4} - 12 x^{3} - 42 x^{2} + 11 = 0

using Newton-Raphson:

x \approx - 0.56098 \dots

Apply long division:

\frac{x ^{4} - 12 x ^{3} - 42 x ^{2} + 11}{x + 0.56098 \dots} = x^{3} - 12.56098 \dots x^{2} - 34.95347 \dots x + 19.60837 \dots

x^{3} - 12.56098 \dots x^{2} - 34.95347 \dots x + 19.60837 \dots \approx 0

Find one solution for

x^{3} - 12.56098 \dots x^{2} - 34.95347 \dots x + 19.60837 \dots = 0

using Newton-Raphson:

x \approx 0.48101 \dots

Apply long division:

\frac{x ^{3} - 12.56098 \dots x ^{2} - 34.95347 \dots x + 19.60837 \dots}{x - 0.48101 \dots} = x^{2} - 12.07996 \dots x - 40.76417 \dots

x^{2} - 12.07996 \dots x - 40.76417 \dots \approx 0

Find one solution for

x^{2} - 12.07996 \dots x - 40.76417 \dots = 0

using Newton-Raphson:

x \approx - 2.74896 \dots

Apply long division:

\frac{x ^{2} - 12.07996 \dots x - 40.76417 \dots}{x + 2.74896 \dots} = x - 14.82892 \dots

x - 14.82892 \dots \approx 0

x \approx 14.82892 \dots

The solutions are

x \approx - 0.56098 \dots, x \approx 0.48101 \dots, x \approx - 2.74896 \dots, x \approx 14.82892 \dots

Graph

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rationalrootstest x^4-4x^3-x^2+14x+10 rational roots

x^{4} - 4 x^{3} - x^{2} + 14 x + 10