The graph of p(x) x^2-x-2 intersects the X-axis
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nswer : The zeros of p(x) are the intersections points of the equation, p(x) = 3x – 2 – x2 with the x-axis. ∴ The number of distinct zeros of p(x) gives the number of distinct intersection points on the X-axis.
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The zeros of p(x) are the intersections points of the equation, p(x) = 3x – 2 – x2 with the x-axis.
∴ The number of distinct zeros of p(x) gives the number of distinct intersection points on the X-axis.
To find the zeros of p(x), consider p(x) = 0
∴3x – 2 – x2 = 0
∴ x2 – 3x+ 2 = 0
∴ x2 – x – 2x+ 2 = 0
∴ x(x – 1) – 2(x – 1) = 0
∴ (x – 1)(x – 2) = 0
∴ x = 1 or x = 2 are the zeros of p(x).
⇒The graph of p(x) intersects X-axis at two points.
The correct option is C.
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