‘The quadratic equations (x^2)-6x+2k=0 and (x^2)-5x+k=0 have a common root A. (i.e. A is a root of both equations)

Show that A=k and hence find the value(s) of k.

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- December 25th 2006, 12:58 PM #1

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- December 25th 2006, 01:32 PM #2

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Let the roots of x^2-6x+2k=0 be A and mu, and the roots of x^2-5x+k=0 be A and lambda

The sum of the roots of x^2-6x+2k=0:

A+mu=6 ...(1)

and the product of the roots is:

A.mu=2k ...(2)

The sum of the roots of x^2-5x+k=0:

A+lambda=5 ...(3)

and the product of the roots is:

A.lambda=k ...(4).

Divide (2) by (3) to get mu=2.lambda ...(5)

Subtract (3) from (1) to get mu-lambda=1 ...(6)

Substituting (5) into (6) gives lambda=1, so by (5) mu=2, and by (2) A=k.

RonL