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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 pointsA. `y=x^(2)+bx+c`B. `y=x^(2)+bx+c-1/2`C. `y=x^(2)+bx+c-1/4`D. `y=x^(2)+bx+c-1/8` |
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Answer» Correct Answer - C 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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