If the roots x^5-40 x^4+P x^3+Q x^2+R x+...

If the roots `x^5-40 x^4+P x^3+Q x^2+R x+S=0` are n G.P. and the sum of their reciprocals is 10, then `|S|` is `4` b. `6` c. `8` d. none of these

Topper's Solved these Questions

BINOMIAL THEOREM
CENGAGE PUBLICATION|Exercise All Questions|363 Videos
CONIC SECTIONS
CENGAGE PUBLICATION|Exercise All Questions|1167 Videos

Similar Questions

Explore conceptually related problems

If S be the sum. P be the product,and R the sum of the reciprocals of n terms in a G.P., Prove that P^2=(S/R)^n

If the sum of the roots of the quadratic equation a x^2+b x+c=0 is equal to the sum of the squares of their reciprocals, then prove that a/c , b/a a n d c/b are in H.P.

If the equation x^2-3p x+2q=0a n dx^2-3a x+2b=0 have a common roots and the other roots of the second equation is the reciprocal of the other roots of the first, then (2q-2b)^2 . a. 36p a(q-b)^2 b. 18p a(q-b)^2 c. 36b q(p-a)^2 d. 18b q(p-a)^2

Let S be the sum, P the product, and R the sum of reciprocals of n terms in a G.P. Prove that P^2R^n=S^ndot

If the roots of the equation x^3+P x^2+Q x-19=0 are each one more that the roots of the equation x^3-A x^2+B x-C=0,w h e r eA ,B ,C ,P ,a n dQ are constants, then find the value of A+B+Cdot

If S be the sum, P the product and R the sum of the reciprocal of n terms in G.P., prove that, p^(2) = ((S)/(R ))^(n) .

If the pth, qth, rth, and sth terms of an A.P. are in G.P., then p-q ,q-r ,r-s are in a. A.P. b. G.P. c. H.P. d. none of these

If alpha,beta are the nonzero roots of a x^2+b x+c=0 and alpha^2,beta^2 are the roots of a^2x^2+b^2x+c^2=0 , then a ,b ,c are in (A) G.P. (B) H.P. (C) A.P. (D) none of these

If (x)=|[x^2+4x-3 2x+4 13] [2x^2+5x-9 4x+5 26] [ 8x^2-6x+1 16 x-6 104]|=a x^3+b x^2+c x+d , then a=3 b. b=0 c. c=0 d. none of these

If the ratio of the roots of the equation x^2+p x+q=0 are equal to ratio of the roots of the equation x^2+b x+c=0 , then prove that p^2c=b^2qdot

CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions

Solve for x :sqrt(x+1)-sqrt(x-1)=1.
Text Solution
|
If x ,y in R a n d2x^2+6x y+5y^2=1,t h e n a. |x|lt=sqrt(5) b. |x|ge...
Text Solution
|
If the roots x^5-40 x^4+P x^3+Q x^2+R x+S=0 are n G.P. and the sum of ...
Text Solution
|
Show that for any triangle with sides a ,b ,and c, 3(a b+b c+c a)<(a+b...
Text Solution
|
For what values of m, does the system of equations 3x+my=m and 2x-5y=2...
Text Solution
|
Show that the square to (sqrt(26-15sqrt(3)))//(5sqrt(2)-sqrt(38+5sqrt(...
Text Solution
|
If alpha,beta are the roots x^2+px+q=0 and gamma,delta are the roots o...
Text Solution
|
Let f(x) =x^2+bx+c, where b,c inR. If f(x) is a factor of both x^4+6x^...
Text Solution
|
If the equation a x^2+b x+c=x has no real roots, then the equation a(a...
Text Solution
|
The value of expression x^4-8x^3+18 x^2-8x+2 when x=2+sqrt(3) a. 2 ...
Text Solution
|
The exhaustive set of values of a for which inequation (a -1)x^2- (a+1...
Text Solution
|
If p ,q ,r ,s are rational numbers and the roots of f(x)=0 are eccentr...
Text Solution
|
If |z-(1/z)|=1, then a. (|z|)(m a x)=(1+sqrt(5))/2 b. (|z|)(m in)=(s...
Text Solution
|
zo is one of the roots of the equation z^n cos theta0+ z^(n-1) cos th...
Text Solution
|
If a0, a1, a2, a3 are all the positive, then 4a0x^3+3a1x^2+2a2x+a3=0 ...
Text Solution
|
If 1,z1,z2,z3,.......,z(n-1) be the n, nth roots of unity and omega b...
Text Solution
|
If a x ^2+b x+c=0 has imaginary roots and a-b+c >0 then the set of poi...
Text Solution
|
All the values of ' a ' for which the quadratic expression a x^2+(a-2)...
Text Solution
|
If the equation z^3 + (3 + i)(z^2) - 3z - (m + i)= 0, m in R , has at ...
Text Solution
|
If a+b+c=0,a^2+b^2+c^2=4,t h e na^4+b^4+c^4 is.
Text Solution
|