Let $\alpha ,\beta $ are the roots of $f\left( x \right) = a{x^2} + bx + c,\;a \ne 0$ and $\Delta = {b^2} - 4ac.\;$ If $\alpha + \beta ,\;{\alpha ^2} + {\beta ^2}\;{\rm{and}}\;{\alpha ^3} + {\beta ^3}$ are in GP, then

JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

1 Easy

1 of 1

Analyzing +4 | -1

Let

\alpha ,\beta

are the roots of

f\left( x \right) = a{x^2} + bx + c,\;a \ne 0

and

\Delta = {b^2} - 4ac.\;

\alpha + \beta ,\;{\alpha ^2} + {\beta ^2}\;\mathrm{and}\;{\alpha ^3} + {\beta ^3}

are in GP, then

View answer and explanation

Correct option: C

c\Delta = 0

Option C (

c\Delta = 0

) is correct because it follows from the condition that

\alpha + \beta

{\alpha ^2} + {\beta ^2}

, and

{\alpha ^3} + {\beta ^3}

are in GP, leading to either

\alpha \beta = 0

\alpha = \beta

Practice All Chapter MCQs →

A=\{1,2,3\}, B=\{3,4\}, C=\{4,5,6\}

{A} \cup({B} \cap {C})

A-(B \cap C)

(B \cup C)-A

a,b,c

a,x,b

b,y,c

{x^2},{b^2},{y^2}

P(x)=1-x+x^2-x^3+\ldots+x^{2012}

y

Q(y)=a_0+a_1 y+\ldots+a_{2012} y^{2012}

y=x-2

\sum\limits_{{i=0}}^{2012} a_i

\log \left(\frac{5 c}{a}\right), \log \left(\frac{3 b}{5 c}\right)

\log \left(\frac{a}{3 b}\right)

A P

a, b

G P

a, b, c

\frac{3}{4}