Question

4. Solve 2x^4+x^3-11x^2+x+2=0

Answer 1

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Answer 2

Answer:

This equation can be reduced to a quadratic equation.

» 2x² + x - 11 + 1/x + 2/x² = 0

» 2 (x² + 1/x²) + (x + 1/x) - 11 = 0

Put, x + 1/x = y

» 2 (y² - 2) + y - 11 = 0

» 2y² + y - 15 = 0

y = -3 & 5/2

x + 1/x = -3, x + 1/x = 5/2

x² + 3x + 1 = 0, 2x² - 5x + 2 = 0

Only second equation has rational roots as 1/2 and 2