f(x) is a quadratic expression such that the coefficient of x2 is negative. If the roots of f(x) = 0 lie in the interval (-1, 1), then which of the following is necessarily true?
Explanation:
Since the coefficient of x2 is negative, the graph of the quadratic function will be downward facing.
Also, since roots lie between -1 and 1, it means the graph will cut the x-axis between x = -1 and x = 1.
Hence, the graph will look something like this.
From the graph it is clear that the value of graph at x = -2 and x = 2 is negative.
Hence, f(-2) and f(2) both will be negative.
Hence, option (d).
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