- Trending Categories
- Data Structure
- Networking
- RDBMS
- Operating System
- Java
- MS Excel
- iOS
- HTML
- CSS
- Android
- Python
- C Programming
- C++
- C#
- MongoDB
- MySQL
- Javascript
- PHP
- Physics
- Chemistry
- Biology
- Mathematics
- English
- Economics
- Psychology
- Social Studies
- Fashion Studies
- Legal Studies

- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who

# Are the following statements 'True' or 'False'? Justify your answers.

If the graph of a polynomial intersects the $ x $-axis at only one point, it cannot be a quadratic polynomial.

Given:

If the graph of a polynomial intersects the \( x \)-axis at only one point, it cannot be a quadratic polynomial.

To do:

We have to find whether the given statement is true or false.

Solution:

We know that,

A quadratic polynomial may touch the X-axis at exactly one point or intersects X-axis at exactly two points or does not touch the X-axis.

Therefore,

If the graph of a polynomial intersects the \( X \)-axis at only one point, then it cannot be a quadratic polynomial.

Hence, the given statement is true.

- Related Articles
- Are the following statements 'True' or 'False'? Justify your answers.If the graph of a polynomial intersects the \( x \)-axis at exactly two points, it need not be a quadratic polynomial.
- Are the following statements 'True' or 'False'? Justify your answers.If the zeroes of a quadratic polynomial \( a x^{2}+b x+c \) are both positive, then \( a, b \) and \( c \) all have the same sign.
- Are the following statements 'True' or 'False'? Justify your answers.If two of the zeroes of a cubic polynomial are zero, then it does not have linear and constant terms.
- Are the following statements 'True' or 'False'? Justify your answers.If all the zeroes of a cubic polynomial are negative, then all the coefficients and the constant term of the polynomial have the same sign.
- Are the following statements 'True' or 'False'? Justify your answers.If all three zeroes of a cubic polynomial \( x^{3}+a x^{2}-b x+c \) are positive, then at least one of \( a, b \) and \( c \) is non-negative.
- Are the following statements 'True' or 'False'? Justify your answers.The only value of \( k \) for which the quadratic polynomial \( k x^{2}+x+k \) has equal zeros is \( \frac{1}{2} \)
- Write whether the following statements are true or false. Justify your answers.Every quadratic equation has at least one real root.
- Write whether the following statements are true or false. Justify your answers.Every quadratic equation has exactly one root.
- Write whether the following statements are true or false. Justify your answers.If the coefficient of \( x^{2} \) and the constant term of a quadratic equation have opposite signs, then the quadratic equation has real roots.
- Write whether the following statements are true or false. Justify your answers.Every quadratic equation has at least two roots.
- Write whether the following statements are true or false. Justify your answers.Every quadratic equations has at most two roots.
- State whether the following statements are true or false. Justify your answer.Points \( \mathrm{A}(3,1), \mathrm{B}(12,-2) \) and \( \mathrm{C}(0,2) \) cannot be the vertices of a triangle.
- Write whether the following statements are true or false. Justify your answers.If the coefficient of $x^2$ and the constant term have the same sign and if the coefficient of $x$ term is zero, then the quadratic equation has no real roots.
- State whether the following statements are true or false. Justify your answer.A circle has its centre at the origin and a point \( P(5,0) \) lies on it. The point \( \mathrm{Q}(6,8) \) lies outside the circle.
- State whether the following statements are true or false. Justify your answer.Point \( P(0,2) \) is the point of intersection of \( y \)-axis and perpendicular bisector of line segment joining the points \( A(-1,1) \) and \( B(3,3) \).

Advertisements