1.

If tangents are drawn to the parabola y=x^(2)+bx+c or b and c fixed real number at the points (i,y_(i)) for i=1,2,…,10. Lt l_(1), l_(2), l_(3)…….l_(9) be the point intersection of tangents at (i,y) and (i+1,y_(i+1)) then the least polynomial satisfying whose graph passes through all nine points

Answer»

`y=X^(2)+bx+c`
`y=x^(2)+bx+c-1/2`
`y=x^(2)+bx+c-1/4`
`y=x^(2)+bx+c-1/8`

SOLUTION :Equation of tangent `(i,y_(j))`
`y=(2i+B)x-i^(2)+c`
Also at `(i+1,y_(i+1)),y=(2i+1)+b)x-(i+1)^(2)+c`
Point of INTERSECTION is `x=(2i+1)/2impliesi=(2x-1)/2`
Put this `i` in any tangent we get `y=x^(2)+bx+c-1/4`


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