Maths-
General
Easy
Question
In the xy-plane, the graph of the polynomial function f crosses the x-axis at exactly two points, (a, 0) and (b, 0), where a and b are both positive. Which of the following could define f?
- f (x) = (x − a) (x - b)
- f (x) = (x + a) (x + b)
- f (x) = (x - a) (x + b)
- f (x) = x(x − a) (x - b)
The correct answer is: f (x) = (x − a) (x - b)
○ The concept used in the question is understanding of quadratic equation.
○ The equation has a two roots.
○ If x satisfy the equation then it is root of that equation.
- Step by step explanation:
○ Given:
Graph of f(x) cross x-axis at exactly two points
(a, 0) and (b, 0).
○ Step 1:
We know that f(x) is quadratic equation.
As it cuts x-axis at two points so it has two roots.
As, it cross x-axis at (a, 0) and (b, 0)
∴ at x = a and x = b, f(x) = 0
Using factor theorem (x - a) and (x - b) are factors of f(x).
So, we can write f(x) as,
f(x) = (x - a) ( x - b)
∴ f(x) = (x - a) ( x - b)
.
- Final Answer:
Correct option.
Option A. f(x) = (x - a) ( x - b).
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