The graph of p(x) = x^{2} - x - 2 intersects | vedclass

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(B) To determine the number of points where the graph of the quadratic polynomial $p(x) = x^{2} - x - 2$ intersects the $X$-axis,we need to find the n

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two distinct points

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(B) To determine the number of points where the graph of the quadratic polynomial $p(x) = x^{2} - x - 2$ intersects the $X$-axis,we need to find the number of real roots of the equation $p(x) = 0$.$1$. Set the polynomial equal to zero: $x^{2} - x - 2 = 0$.$2$. Calculate the discriminant $D = b^{2} - 4ac$,where $a = 1$,$b = -1$,and $c = -2$.$3$. $D = (-1)^{2} - 4(1)(-2) = 1 + 8 = 9$.$4$. Since $D > 0$,the quadratic equation has two distinct real roots.$5$. Therefore,the graph of the polynomial intersects the $X$-axis at two distinct points.

The graph of $p(x) = x^{2} - x - 2$ intersects the $X$-axis at:

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