Question

Assertion (A): If the graph of a polynomial touches x-axis at only one point, then the polynomial cannot be a quadratic polynomial.

Reason (R): A polynomial of degree n(n >1) can have at most n zeroes.

विकल्प

• Both, Assertion (A) and Reason (R) are true and Reason (R) is correct explanation of Assertion (A).

• Both, Assertion (A) and Reason (R) are true but Reason (R) is not correct explanation for Assertion (A).

• Assertion (A) is true but Reason (R) is false.

• Assertion (A) is false but Reason (R) is true.

Answer 1

Assertion (A) is false but Reason (R) is true.

Explanation: 

A quadratic polynomial is a second-degree polynomial, typically written in the form ax² + bx + c where a, b, and c are constants, and a ≠ 0. It can have a maximum of two zeroes, which are the values of x that make the polynomial equal to zero. If the graph of a quadratic polynomial touches the x-axis at only one point, it means the polynomial has a repeated root or double root. This occurs when the discriminant of the quadratic equation is zero (b² − 4ac = 0), resulting in a single, unique solution. Therefore, the assertion that a polynomial cannot be quadratic if it touches the x-axis at only one point is incorrect, as such a case is possible. The reason given is correct, but it does not justify the assertion.