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Maths-

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Question

Suppose A,B,C are defined as $A equals a to the power of 2 end exponent b plus a b to the power of 2 end exponent minus a to the power of 2 end exponent c minus a c to the power of 2 end exponent comma B equals b to the power of 2 end exponent c plus b c to the power of 2 end exponent minus a to the power of 2 end exponent b minus a b to the power of 2 end exponent comma$ and $C equals a to the power of 2 end exponent c plus c to the power of 2 end exponent a minus c b to the power of 2 end exponent minus c to the power of 2 end exponent b text where end text a greater than b greater than c greater than 0$ and the equation $A x to the power of 2 end exponent plus B x plus C equals 0$ has equal roots, then a,b,c are in

A.P
G.P
A.G.P
H.P

The correct answer is: H.P

Related Questions to study

Consider the quadratic equation $a x to the power of 2 end exponent minus b x plus c equals 0 comma a comma b comma c element of N$ If the given equation has two distinct real roots belonging to (1, 2)then

Consider the quadratic equation $a x to the power of 2 end exponent minus b x plus c equals 0 comma a comma b comma c element of N$ If the given equation has two distinct real roots belonging to (1, 2)then

If the sum of the roots of the quadratic equation, $a x to the power of 2 end exponent plus b x plus c equals 0$ is equal to sum of the squares of their reciprocals, then $fraction numerator a over denominator c end fraction comma fraction numerator b over denominator a end fraction comma fraction numerator c over denominator b end fraction$ are in :

If the sum of the roots of the quadratic equation, $a x to the power of 2 end exponent plus b x plus c equals 0$ is equal to sum of the squares of their reciprocals, then $fraction numerator a over denominator c end fraction comma fraction numerator b over denominator a end fraction comma fraction numerator c over denominator b end fraction$ are in :

All possible quadratic equations $a x to the power of 2 end exponent plus b x plus 1 equals 0$ taking $a stack I with hat on top left curly bracket 1 , 2 comma 3 comma horizontal ellipsis n right curly bracket comma b stack I with hat on top left curly bracket 1 comma negative 2 comma negative 3 comma horizontal ellipsis horizontal ellipsis minus n right curly bracket$ and if $open parentheses a subscript i end subscript comma b subscript i end subscript close parentheses i equals 1 , 2 comma 3 comma horizontal ellipsis.. n$ represent solution sets of these equations then $text å end text fraction numerator 1 over denominator a subscript i end subscript end fraction plus a to the power of ring operator end exponent fraction numerator 1 over denominator b subscript i end subscript end fraction$ equals

All possible quadratic equations $a x to the power of 2 end exponent plus b x plus 1 equals 0$ taking $a stack I with hat on top left curly bracket 1 , 2 comma 3 comma horizontal ellipsis n right curly bracket comma b stack I with hat on top left curly bracket 1 comma negative 2 comma negative 3 comma horizontal ellipsis horizontal ellipsis minus n right curly bracket$ and if $open parentheses a subscript i end subscript comma b subscript i end subscript close parentheses i equals 1 , 2 comma 3 comma horizontal ellipsis.. n$ represent solution sets of these equations then $text å end text fraction numerator 1 over denominator a subscript i end subscript end fraction plus a to the power of ring operator end exponent fraction numerator 1 over denominator b subscript i end subscript end fraction$ equals

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Let $f left parenthesis x right parenthesis equals fraction numerator open parentheses 2 x to the power of 3 end exponent minus 9 x to the power of 2 end exponent plus 12 x plus 3 close parentheses left parenthesis x minus a right parenthesis over denominator left parenthesis x minus a right parenthesis end fraction$ If range of f(x) is a proper subset of the set of real numbers, then the most exhaustive set in which a lies is

Let $f left parenthesis x right parenthesis equals fraction numerator open parentheses 2 x to the power of 3 end exponent minus 9 x to the power of 2 end exponent plus 12 x plus 3 close parentheses left parenthesis x minus a right parenthesis over denominator left parenthesis x minus a right parenthesis end fraction$ If range of f(x) is a proper subset of the set of real numbers, then the most exhaustive set in which a lies is

If $open parentheses b to the power of 2 end exponent minus 4 a c close parentheses to the power of 2 end exponent open parentheses 1 plus 4 a to the power of 2 end exponent close parentheses less than 64 a to the power of 2 end exponent comma a less than 0 comma$ then maximum value of quadratic expression $a x to the power of 2 end exponent plus b x plus c$ is always less than

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Analyze the following graph of $f to the power of ´ end exponent left parenthesis x right parenthesis$ the which is incorrect about $f left parenthesis x right parenthesis text for end text alpha less than x less than beta$

Analyze the following graph of $f to the power of ´ end exponent left parenthesis x right parenthesis$ the which is incorrect about $f left parenthesis x right parenthesis text for end text alpha less than x less than beta$

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If one root is square of other root of equation $x to the power of 2 end exponent plus p x plus q equals 0 comma q element of R$ then condition on

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Statement -1 : There exists only one real value of ‘k’ for which the real roots of the equation $k x to the power of 3 end exponent plus 3 x to the power of 2 end exponent minus 3 x plus 1 equals 0$ are in H.P. because
Statement - 2 : For a cubical equation $a x to the power of 3 end exponent plus b x to the power of 2 end exponent plus c x plus d equals 0 comma$ if b, c and d are non zero real and constant, then we can have only one real value of ‘a’ for which all real roots of $a x to the power of 3 end exponent plus b x to the power of 2 end exponent plus c x plus d equals 0$ are in H.P.

Statement -1 : There exists only one real value of ‘k’ for which the real roots of the equation $k x to the power of 3 end exponent plus 3 x to the power of 2 end exponent minus 3 x plus 1 equals 0$ are in H.P. because
Statement - 2 : For a cubical equation $a x to the power of 3 end exponent plus b x to the power of 2 end exponent plus c x plus d equals 0 comma$ if b, c and d are non zero real and constant, then we can have only one real value of ‘a’ for which all real roots of $a x to the power of 3 end exponent plus b x to the power of 2 end exponent plus c x plus d equals 0$ are in H.P.

Consider a triangle ABC. BE and CF are the medians drawn through the angular points B and C respectively and G is the centroid of the $capital delta$ ABC.
Statement – 1: If the points, A, E, G, F are concyclic then $angle A$ must be acute. because
Statement – 2: The medians of a triangle divide triangle into area wise two equal parts.

Consider a triangle ABC. BE and CF are the medians drawn through the angular points B and C respectively and G is the centroid of the $capital delta$ ABC.
Statement – 1: If the points, A, E, G, F are concyclic then $angle A$ must be acute. because
Statement – 2: The medians of a triangle divide triangle into area wise two equal parts.

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A density bottle weighs 24 g when filled with water and 31 g when filled with a liquid of density $8 g divided by c. c$ Then the mass of the density bottle is

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