If the roots of ab-c x2-bc-a x-ca-b-0 are equal- then a- b- c are inA- G-P-B- H-P-C- A-G-P-D- A-P-

The correct option is B H.P. Sum of coefficients = 0 Therefore 1, c(a b)/a(b c) are roots Given they are equal = gt; 1 = c(a b)/a(b c) . hence they are in H. ...

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Standard X

Mathematics

Roots of Quadratic Equation

If the roots ...

Question

If the roots of a(b-c) $x^{2}$ +b(c-a)x+c(a-b)=0 are equal, then a,b,c are in

A.P.

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G.P.

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H.P.

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A.G.P.

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Solution

The correct option is C
H.P.

Sum of coefficients = 0

Therefore 1, $\frac{c (a - b)}{a (b - c)}$ are roots

Given they are equal

=> 1 = $\frac{c (a - b)}{a (b - c)}$ . hence they are in H.P

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If the roots of a(b-c)x2+b(c-a)x+c(a-b)=0 are equal, then a,b,c are in

The correct option is C H.P. Sum of coefficients = 0 Therefore 1, c(a−b)a(b−c) are roots Given they are equal => 1 = c(a−b)a(b−c) . hence they are in H.P

If the roots of a(b-c) $x^{2}$ +b(c-a)x+c(a-b)=0 are equal, then a,b,c are in

The correct option is C
H.P.

Sum of coefficients = 0

Therefore 1, $\frac{c (a - b)}{a (b - c)}$ are roots

Given they are equal

=> 1 = $\frac{c (a - b)}{a (b - c)}$ . hence they are in H.P