If the graph of a polynomial intersects the x-axis at exactly two points, it need not be a quadratic polynomial. Is the statement true or false? Justify your answer
Solution:
Given, the graph of a polynomial intersects the x-axis at exactly two points.
We have to determine whether the graph needs to be a quadratic polynomial or not.
A quadratic polynomial has less than or equal to two roots.
When the graph line of a polynomial intersects the x axis at exactly two points, it implies that the polynomial has two equal roots or greater than two roots.
Therefore, it cannot be a quadratic polynomial.
✦ Try This: If the graph of a polynomial x² - 5x + 4 intersects the x-axis at exactly two points, it need not be a quadratic polynomial. Is the statement true or false? Justify your answer
Given, the graph of a polynomial x² - 5x + 4 intersects the x-axis at exactly two points.
We have to determine whether the graph needs to be a quadratic polynomial or not.
x² - 5x + 4
= x² - 4x - x + 4
Taking out the common term
= x(x - 4) - 1(x - 4)
= (x - 4)(x - 1)
A quadratic polynomial has less than or equal to two roots.
When the graph line of a polynomial intersects the x axis at exactly two points, it implies that the polynomial has two equal roots or greater than two roots
Therefore, it cannot be a quadratic polynomial
The statement is true
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 2
NCERT Exemplar Class 10 Maths Exercise 2.2 Problem 2 (iii)
If the graph of a polynomial intersects the x-axis at exactly two points, it need not be a quadratic polynomial. Is the statement true or false? Justify your answer
Summary:
If the graph of a polynomial intersects the x-axis at exactly two points, it need not be a quadratic polynomial. The statement is true
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