Question

In quadratic equation ax^2+bx+c=0 ...
(sequence and series)

Answer 1

IN quadratic equation ax^2+bx+c=0. If alpha,beta are the roots of the equation d=b^2-4ac and alpha+beta,alpha^2+beta^2,alpha^3+beta^3 are in GP them

Answer 2

A)d is not equal to zero
B)bd=0
C=cd=0
D)d=0

Answer 3

@dan815 @ganeshie8 @ikram002p @Miracrown

Answer 4

@nincompoop

Answer 5

IIT advanced question

Answer 6

@Kainui

Answer 7

establish below first :

\(\large \alpha + \beta = -\dfrac{b}{a}\)

\(\large \alpha^2 + \beta^2 = \dfrac{b^2}{a^2} - 2\dfrac{c}{a}\)

\(\large \alpha^3 + \beta^3 = -\dfrac{b}{a}\left( \dfrac{b^2}{a^2} - 3\dfrac{c}{a}\right)\)

Answer 8

yes

Answer 9

i established these

Answer 10

after that use the geometric mean to get a relation in a,b,c
simplifying it yields \(b^2-4ac = 0\)
or, \(d = 0\)

Answer 11

i got the same answer but the answer is given as cd=0

Answer 12

\[does \Delta\] or d makes any difference to u

Answer 13

@ganeshie8

Answer 14

can you take a screenshot and attach if possible - just for clarity

Answer 15

OK