# If one of the roots of the equation : (k-1) x^2 - 5x + 2 = 0 is the multiplicative inverse of the root, then the value of k= ???

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The given equation is `(k-1) x^2 - 5x + 2 = 0` . Comparing it with `ax^2+bx+c=0` ,

Product of the roots=`c/a=2/(k-1)`

Again, since one of the roots of the given equation is the multiplicative inverse of the other root,

Hence, product of the roots=`1`

By condition,

`2/( k-1)=1`

`rArr 2=k-1`

`rArr k=2+1=3`

**Therefore, the value of k is 3.**

Given Equation: `(k-1)x^2 - 5x +2 = 0`

Also it is given that if one root is "x" then other root is "1/x" ( Multiplicative inverse of x)

To find: Value of K

Solution:

If the equation is `ax^2 + bx + c = 0`

then, product of roots is `c/a`

Substituting the values of in the given Equation we get

`x xx (1/x) = (2 / (k-1))`

`=> 1 = 2/ (k-1)`

`=> 1 xx (k-1) = 2`

`=> k - 1 = 2`

`=> k = 2 + 1`

`=> k = 3`

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The given equation is . Comparing it with ,

a=(k-1), b=-5, c=2

Product of the roots=

Again, since one of the roots of the given equation is the multiplicative inverse of the other root,(x * 1/x =1)

Hence, product of the roots=1

By condition,

**Therefore, the value of k is 3.**