biquadratic equation......

\hspace{-16}$If $\bf{r_{1}\;,r_{2}\;,r_{3}\;,r_{4}}$ are the roots of the equation $\bf{4x^4-ax^3+bx^2-cx+5=0}$\\\\\\ Where $\bf{r_{1}\;,r_{2}\;,r_{3}\;,r_{4}>0}$ and satisfy $\bf{\frac{r_1}{2} + \frac{r_2}{4} + \frac{r_3}{5} + \frac{r_4}{8} = 1}$\\\\\\ Then find value of $\bf{r_{1}\;,r_{2}\;,r_{3}\;,r_{4}}$

6 Answers

1
rishabh ·

1,2,12,54

1057
Ketan Chandak ·

simply.....the product of the roots of a polynomial is equal to constant termco-efficient of highest power of x

262
Aditya Bhutra ·

right ,rishab .

Apply AM ≥GM for r1/2 , r2 /4 , r3/5 , r4/8

1
rishabh ·

@aditya it is rishabh ! :P

@ketan he asked for roots not product of roots :P

1057
Ketan Chandak ·

@rishabh...the comma and the full stop all look the same... :P

1708
man111 singh ·

Thanks Rishabh, Aditiya

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