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The sum of the abscissae of the points where the curves,

y=kx^{2}+(5k+3)x+6k+5,(k\epsilon R), touch the x-axis,is equal to :

  • Option 1)

    -\frac{4}{3}

  • Option 2)

    -\frac{19}{3}

  • Option 3)

    -\frac{10}{3}

  • Option 4)

    \frac{5}{3}

 

Answers (1)

best_answer

 

Abscissa -

The distance from a point to the vertical or y-axis.

- wherein

The x coordinate.

 

 

For touching x-axis, y=0

So, kx^2+(5k+3)x+6k+5=0

Discriminant =0 for touching x

\Rightarrow \left ( 5k+3 \right )^2-4k\left ( 6k+5 \right )= 0

\Rightarrow k^2+10k+9= 0

\Rightarrow (k+9)(k+1)= 0

\Rightarrow k=-9,-1

So, -x^2-2x-1=0  &  -9x^2-42x-49=0  are equations

\Rightarrow x=-1,x=-7/3\Rightarrow Sum=\frac{-10}{3}


Option 1)

-\frac{4}{3}

Option 2)

-\frac{19}{3}

Option 3)

-\frac{10}{3}

Option 4)

\frac{5}{3}

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Plabita

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