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10 cards from this deck
ax3+bx2+cx+d=0ax^3 + bx^2 + cx + d = 0ax3+bx2+cx+d=0 where a≠0a \neq 0a=0
Equation would reduce to quadratic or lower degree
(x−a)(x - a)(x−a) is a factor of the polynomial
Use factor theorem to find one factor
Simple integers like ±1\pm 1±1, ±2\pm 2±2, ±3\pm 3±3
Divide cubic by this factor to get quadratic factor
When quadratic factor cannot be factorised by inspection
x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}x=2a−b±b2−4ac
3 real solutions
Only 1 real solution (from factor theorem)
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