Solve the equation. 20x^{3}+8x^{2}-35x-14=0

vomiderawo

vomiderawo

Answered question

2021-11-18

Solve the equation.
20x3+8x235x14=0

Answer & Explanation

Jennifer Hill

Jennifer Hill

Beginner2021-11-19Added 10 answers

Step 1
Solve the equation.
20x3+8x235x14=0
Step 2
We have 20x3+8x235x14=0
20x3+8x235x14=0
4x2(5x+2)7(5x+2)=0
(5x+2)(4x27)=0
(5x+2)=0 or (4x27)=0
5x=2 or 4x2=7
x=25 or x=74
Hence, x=25 or x=74
Knes1997

Knes1997

Beginner2021-11-20Added 11 answers

20x3+8x235x14=0
With the Ratio Root Theorem, all polynomial ratio roots are in the form pq, when p divide the constant pronunciation - 14 and q divide the precursor coefficient 20. List all candidates pq.
±710,±75,±145,±72,±7,±14,±720,±74,±110,±15,±25,±12,±1,±2,±120,±14
Find one such root by trying all integer values, starting with the smallest according to the absolute value. If no integer root is found, try a fraction.
x=25
With the Factor theorem, x-k is a polynomial factor for each root k. Divide 20x3+8x235x14 by 5(x+25)=5x+2 to obtain 4x27. Solve the equation where the result is equal to 0.
4x27=0
All form equations ax2+bx+c=0 can be solved using the quadratic formula: b±b24ac2a. Replace4 for a, 0 for b and - 7 for c in a quadratic formula.
x=0±024×4(7)2×4
Do the calculations.
x=0±478
Solve the equation 4x27=0 when ± is plus and when ± is minus.
x=72
x=72
List all the solutions found.
x=25
x=72
x=72

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