Consider the equation 3 x4-18 x3+p x2-8 q x+3 q=0. The equation has only positive real roots then the value of (p/q) is

Question

Consider the equation 3 x4-18 x3+p x2-8 q x+3 q=0. The equation has only positive real roots then the value of (p/q) is (A) (1/8) (B) 4 (C) (1/4) (D) 8

Tardigrade Admin · Accepted Answer

text A.M. =(x1+x2+x3+x4/4)=(18/3 × 4)=(3/2) text H.M. =(4/8 / 3)=(12/8)=(3/2) text A.M. = text H.M. ⇒ x1=x2=x3=x4=(3/2) p =(81/2) and q =(81/16).

Q. Consider the equation $3 x^{4} - 18 x^{3} + p x^{2} - 8 q x + 3 q = 0$ . The equation has only positive real roots then the value of $\frac{p}{q}$ is

$\frac{1}{8}$

4

$\frac{1}{4}$

8

$A.M. = \frac{x _{1} + x _{2} + x _{3} + x _{4}}{4} = \frac{18}{3 \times 4} = \frac{3}{2}$
$H.M. = \frac{4}{8/3} = \frac{12}{8} = \frac{3}{2}$
$A.M. = H.M. \Rightarrow x_{1} = x_{2} = x_{3} = x_{4} = \frac{3}{2}$
$p = \frac{81}{2}$ and $q = \frac{81}{16}$ .

Q. Consider the equation 3x4−18x3+px2−8qx+3q=0. The equation has only positive real roots then the value of qp​ is

81​

4

41​

8

A.M. =4x1​+x2​+x3​+x4​​=3×418​=23​ H.M. =8/34​=812​=23​ A.M. = H.M. ⇒x1​=x2​=x3​=x4​=23​ p=281​ and q=1681​.

Q. Consider the equation $3 x^{4} - 18 x^{3} + p x^{2} - 8 q x + 3 q = 0$ . The equation has only positive real roots then the value of $\frac{p}{q}$ is

$\frac{1}{8}$

$\frac{1}{4}$

$A.M. = \frac{x _{1} + x _{2} + x _{3} + x _{4}}{4} = \frac{18}{3 \times 4} = \frac{3}{2}$
$H.M. = \frac{4}{8/3} = \frac{12}{8} = \frac{3}{2}$
$A.M. = H.M. \Rightarrow x_{1} = x_{2} = x_{3} = x_{4} = \frac{3}{2}$
$p = \frac{81}{2}$ and $q = \frac{81}{16}$ .