Question

Which of the following is not the graph of a quadratic polynomial ?

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Answer 1

For a quadratic polynomial, $a{x}^2+bx+c$, the zeros are precisely the x-coordinates of the points where the graph representing $y=a{x}^2+bx+c$ intersects the x-axis.
The graph has one of the two shapes either open upwards like ∪ (parabolic shape) or open downwards like ∩ (parabolic shape) depending on whether a > 0 or a < 0.
Three cases are thus possible:
a) graph cuts x-axis at two distinct points (two zeroes)
b) graph cuts the x-axis at exactly one point (one zero)
c) the graph is either completely above the x-axis or completely below the x-axis (no zeroes)
In option (d), the graph is cutting the x-axis at three distinct points and it is not a parabola opening either upwards or downwards.
So, option (d) does not represent the graph of a quadratic polynomial.

Hence, the correct answer is option D.