What is -10x^4+70x^3-60x^2>0 ?

The solution to -10x^4+70x^3-60x^2>0 is 1<x<6

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-10x^4+70x^3-60x^2>0

- 10 x^{4} + 70 x^{3} - 60 x^{2} > 0

1 < x < 6

Interval Notation

(1, 6)

Solution steps

- 10 x^{4} + 70 x^{3} - 60 x^{2} > 0

Rewrite in standard form

- x^{4} + 7 x^{3} - 6 x^{2} > 0

Factor

- x^{4} + 7 x^{3} - 6 x^{2} : - x^{2} (x - 1) (x - 6)

- x^{2} (x - 1) (x - 6) > 0

Multiply both sides by

- 1

(reverse the inequality)

(- x^{2} (x - 1) (x - 6)) (- 1) < 0 \cdot (- 1)

Simplify

x^{2} (x - 1) (x - 6) < 0

Identify the intervals

1 < x < 6

\frac{( 3 x + 4 )}{( x - 2 )} < 1

\frac{x + 1}{x} > 3

\frac{( x + 3 )}{3} \cdot \frac{4}{( x + 2 )} > \frac{x}{3}

\frac{( ( x - 1 ) ^{2} )}{( x - 2 )} \leq 0

\frac{x}{( x + 1 )} > \frac{1}{x}