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Mathematics
Sebastian
11 March, 19:50
F (x) = 10x3 - 13x² + 12x + 3
+1
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Lydia Cobb
11 March, 21:46
0
x = - 1/5
Step-by-step explanation:
Solve for x over the real numbers:
10 x^3 - 13 x^2 + 12 x + 3 = 0
The left hand side factors into a product with two terms:
(5 x + 1) (2 x^2 - 3 x + 3) = 0
Split into two equations:
5 x + 1 = 0 or 2 x^2 - 3 x + 3 = 0
Subtract 1 from both sides:
5 x = - 1 or 2 x^2 - 3 x + 3 = 0
Divide both sides by 5:
x = - 1/5 or 2 x^2 - 3 x + 3 = 0
Divide both sides by 2:
x = - 1/5 or x^2 - (3 x) / 2 + 3/2 = 0
Subtract 3/2 from both sides:
x = - 1/5 or x^2 - (3 x) / 2 = - 3/2
Add 9/16 to both sides:
x = - 1/5 or x^2 - (3 x) / 2 + 9/16 = - 15/16
Write the left hand side as a square:
x = - 1/5 or (x - 3/4) ^2 = - 15/16
(x - 3/4) ^2 = - 15/16 has no solution since for all x on the real line, (x - 3/4) ^2 >=0 and - 15/16<0:
Answer: x = - 1/5
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