How do I solve x^{4}-x^{3}-19x^{2}+49x-30=0?

tressudasikx

tressudasikx

Answered question

2022-03-03

How do I solve
x4x319x2+49x30=0?

Answer & Explanation

Chance Mill

Chance Mill

Beginner2022-03-04Added 8 answers

Step 1
x=1 makes the equation equal to 0
x4x319x2+49x30=0
x3(x1)(19x249x+30)=0
x3(x1)(19x219x30x+30)=0
x3(x1)[19x(x1)30(x1)]=0
(x1)(x319x+30)=0
(x1)[x32x2+2x219x+30]=0
(x1)[x2(x2)+2x24x15x+30]=0
(x1)[x2(x2)+2x(x2)15(x2)]=0
(x1)(x2)(x2+2x15)=0
(x1)(x2)(x+5)(x3)=0
x=5, 1, 2, 3
Lillie-May Sutton

Lillie-May Sutton

Beginner2022-03-05Added 3 answers

Step 1
Given:
x4x319x2+49x30=0
Starting with the sum of the coefficients
1119+4930=0
so x=1 is a solution and x1 is a factor. Factor it out to get
(x1)(x319x+30)=0
x319x+30=0
has the roots α, β, γ where αβγ=30
α+β+γ=0 and αβ+γα+βγ=19
2+3±5=0,
2×3×5=30
and checking
2×3±5×2+3×5=19
So the solutions for x are 1, 2, 3 and 5

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