If the equation x^4−4x^3+ax^2+bx+1=0 has four positive roots then a=? and b=?

Gauge Roach

Gauge Roach

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2022-08-14

If the equation x 4 4 x 3 + a x 2 + b x + 1 = 0 has four positive roots then a=? and b=?

Answer & Explanation

Preston Espinoza

Preston Espinoza

Beginner2022-08-15Added 8 answers

( x x 1 ) ( x x 2 ) ( x x 3 ) ( x x 4 )
= x 4 x 3 ( 4 i 1 x i ) + x 2 ( 4 i > j 1 x i x j ) x ( 4 i > j > k 1 x i x j x k ) + x 1 x 2 x 3 x 4
If x i > 0 , 1 i 4 the coefficient of x 2 must be >0 and that of x must be <0

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