thegraph of polynomial p(x) is x^3-4x intersects x axis at ________ distinct points. options a=0 b-1 c-2 d -3
Answers
Answer:
p(x) intersects x-axis at two distinct points i.e at -2 and 2
Step-by-step explanation:
Given p(x)=x³-4x
x³-4x=0
x³=4x
x²=4
x=2 and x=-2
p(x) intersects x-axis at two distinct points
p(x) graph will look like this..
Answer:
A polynomial is a mathematical expression consisting of variables and coefficients involving only the operations of addition, subtraction, multiplication, and non-negative integer exponents. In other words, a polynomial is a sum of terms, each of which is a constant or a variable raised to a power.
Step-by-step explanation:
The graph of a polynomial function intersects the x-axis at the point where the function value equals zero. Therefore, to find the number of distinct points where the polynomial p(x) = x^3 - 4x intersects the x-axis, we need to solve the equation p(x) = 0.
x^3 - 4x = 0
Factorizing out x, we get:
x(x^2 - 4) = 0
Now we have two factors: x and (x^2 - 4). The first factor, x, gives us one solution: x = 0. The second factor, (x^2 - 4), can be further factorized as (x - 2)(x + 2), giving us two additional solutions: x = 2 and x = -2.
Therefore, the polynomial p(x) = x^3 - 4x intersects the x-axis at three distinct points: x = 0, x = 2, and x = -2.
In conclusion, the answer to the question is option D: -3 is impossible since the polynomial intersects the x-axis at three distinct points.
To learn more about polynomials, click on the given link.
https://brainly.in/question/7881602
To learn more about non-negative integer exponents, click on the given link.
https://brainly.in/question/19163130
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