Question

find no. of solutions of equation less than 10

sgn(x³-4x²+3x)=1

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Answer 1

$\huge\star{\mathbb{\underline{\underline{\red{Answer}}}}}$

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We know that

when sgn(x)=1

x>0

so,

$\implies$x³-4x²+3x>1

$\implies$ x(x²-4x+3)>0

Quadratic solutions-

(x-1)(x-3)

x(x-1)(x-3)>0

Here we have three solutions for wavy curve

see the attachment for wavy curve

x€(0,1) U (3,$\infty$ )

Therefore

Solutions-

$\implies$4,5,6,7,8,9

$\huge{\underline{\boxed{\boxed{6 \: solutions}}}}$

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Answer 2

Answer:

We know that

when sgn(x)=1

x>0

so,

\implies⟹ x³-4x²+3x>1

\implies⟹ x(x²-4x+3)>0

Quadratic solutions-

(x-1)(x-3)

x(x-1)(x-3)>0

Here we have three solutions for wavy curve

see the attachment for wavy curve

x€(0,1) U (3,\infty∞ )

Therefore

Solutions-

\implies⟹ 4,5,6,7,8,9

\huge{\underline{\boxed{\boxed{6 \: solutions}}}}

6solutions