If the graph of a polynomial intersects the x-axis at only one point, it cannot be a quadratic polynomial. Is the following statement ‘True’ or ‘False’? Justify your answer
Solution:
Given, the graph of a polynomial intersects the x-axis at only one point.
We have to determine whether the graph represents a quadratic polynomial or not.
The quadratic polynomials are the polynomials of the form (x+a)² and (x-a)² which have only equal roots and the graph of these polynomials cuts the x-axis at only one point.
The quadratic polynomials have at most two zeros but not exactly two zeroes.
When the graph line of a polynomial intersects the x axis at only one point, it implies that the polynomial has two equal roots where discriminant=0.
Therefore, the graph can represent a quadratic polynomial.
✦ Try This: If the graph of a polynomial x² + 2x + 1 intersects the x-axis at only one point, it cannot be a quadratic polynomial. Is the following statement ‘True’ or ‘False’? Justify your answer
Given, the graph of a polynomial x² + 2x + 1 intersects the x-axis at only one point.
We have to determine whether the graph represents a quadratic polynomial or not.
x² + 2x + 1
= x² + x + x + 1
Taking out the common terms
= x(x + 1) + 1(x + 1)
= (x + 1)(x + 1)
So we get
x + 1 = 0
x = -1
Therefore, if the graph of a polynomial x² + 2x + 1 intersects the x-axis at only one point, it cannot be a quadratic polynomial. The statement is false
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 2
NCERT Exemplar Class 10 Maths Exercise 2.2 Problem 2 (ii)
If the graph of a polynomial intersects the x-axis at only one point, it cannot be a quadratic polynomial. Is the following statement ‘True’ or ‘False’? Justify your answer
Summary:
If the graph of a polynomial intersects the x-axis at only one point, it cannot be a quadratic polynomial. The statement is false
☛ Related Questions:
- If two of the zeroes of a cubic polynomial are zero, then it does not have linear and constant terms . . . .
- If all the zeros of a cubic polynomial are negative, then all the coefficients and the constant term . . . .
- If all three zeros of a cubic polynomial x³ + ax² - bx + c are positive, then at least one of a, b a . . . .
visual curriculum