Let a and b be roots of x^2 - 3x + p = 0 and | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Given that $a$ and $b$ are roots of $x^2 - 3x + p = 0$,so $a + b = 3$ and $ab = p$.Given that $c$ and $d$ are roots of $x^2 - 12x + q = 0$,so $c +

Vedclass · Accepted Answer

$17 : 15$

Vedclass · Answer

(C) Given that $a$ and $b$ are roots of $x^2 - 3x + p = 0$,so $a + b = 3$ and $ab = p$.Given that $c$ and $d$ are roots of $x^2 - 12x + q = 0$,so $c + d = 12$ and $cd = q$.Since $a, b, c, d$ are in an increasing $G$.$P$.,let the terms be $a, ar, ar^2, ar^3$ where $r > 1$.Then $a + b = a(1 + r) = 3$ and $ab = a^2r = p$.Also $c + d = ar^2(1 + r) = 12$ and $cd = a^2r^5 = q$.Dividing the sum equations: $\frac{ar^2(1 + r)}{a(1 + r)} = \frac{12}{3} \Rightarrow r^2 = 4$. Since the $G$.$P$. is increasing,$r = 2$.Now,substitute $r = 2$ into the sum equations: $a(1 + 2) = 3 \Rightarrow 3a = 3 \Rightarrow a = 1$.Then $b = ar = 2$,$c = ar^2 = 4$,and $d = ar^3 = 8$.Calculate $p$ and $q$: $p = ab = 1 	imes 2 = 2$ and $q = cd = 4 	imes 8 = 32$.The ratio $(q + p) : (q - p) = (32 + 2) : (32 - 2) = 34 : 30 = 17 : 15$.

Let $a$ and $b$ be roots of $x^2 - 3x + p = 0$ and let $c$ and $d$ be the roots of $x^2 - 12x + q = 0$,where $a, b, c, d$ form an increasing $G$.$P$. Then the ratio of $(q + p) : (q - p)$ is equal to

Similar Questions

The sum of the series $\frac{1}{1 + \sqrt{2}} + \frac{1}{\sqrt{2} + \sqrt{3}} + \frac{1}{\sqrt{3} + \sqrt{4}} + \dots$ up to $15$ terms is

The sum of the infinite series $\frac{1}{9} + \frac{1}{18} + \frac{1}{30} + \frac{1}{45} + \frac{1}{63} + ..........\infty$ is equal to :-

The $H.M.$ between the roots of the equation $x^2 - 10x + 11 = 0$ is

If $S_n = 1 + \frac{1}{2} + \frac{1}{2^2} + \dots + \frac{1}{2^{n-1}}$,then the least integral value of $n$ such that $2 - S_n < \frac{1}{100}$ is

If $a_1, a_2, a_3, .... a_{21}$ are in $A.P.$ and $a_3 + a_5 + a_{11} + a_{17} + a_{19} = 10$,then the value of $\sum_{r=1}^{21} a_r$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module