The determinant $\Delta = \left| {\begin{array}{*{20}{c}} a&b&{a\alpha + b}\\ b&c&{b\alpha + c}\\ {a\alpha + b}&{b\alpha + c}&0 \end{array}} \right|$ is equal to zero, if

$\alpha $ is a root of $a{x^2} + bx + c = 0$

JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

1 Easy

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Analyzing +4 | -1

The determinant

\Delta = \left| {\begin{array}{cccccccccccccccccccc} a&b&{a\alpha + b}\\ b&c&{b\alpha + c}\\ {a\alpha + b}&{b\alpha + c}&0 \end{array}} \right|

is equal to zero, if

View answer and explanation

Correct option: B

a,b,c

are in G.P.

Option B (

a,b,c

are in G.P.) is correct because the determinant simplifies to zero when

b^2 = ac

, which is the condition for a geometric progression.

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}