2X^3 + 11X^2 = 6X
2X^3 + 11X^2 - 6X = 0
factor out an X
X(2X^2 + 11X - 6) = 0
Now, for that quadratic equation I always go quadratic formula. Discriminant looks good for two real roots.
X = -b (+/- ) sqrt(b^2-4ac)/2a
a = 2
b = 11
c = - 6
X = - 11 (+/-) sqrt[11^2 - 4(2)(-6)]/2(2)
X = - 11 (+/-) sqrt(169)/4
X = [- 11 (+/-) 13]/4
X = 0
X = 1/2
X = - 6
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x = -28 / -11^2
The discriminant, for what it is worth in an example such as this, is 11.
Dividend: 4x^4 -x^3 +17x^2 +11x +4 Divisor: 4x +3 Quotient: x^3 -x^2 +5x -1 Remainder: 7
2x2 + 11x + 15 = (x + 3)(2x + 5).
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