Question

Q.No: 1. The graph of a cubic polynomial cuts the x- axis at atmost ______ points.

Answer 1

The graph of a cubic polynomial cuts the x - axis at almost three points.

Concepts :

• A polynomial is an algebraic expression that consists of variables and coefficients. It involves only the operations of addition, subtraction, multiplication and non-negative integral exponents of variables.
• If we assume, y = P(x) is an polynomial expression, and plot the graph of it, graph cuts the x - axis that shows value of x. and it cuts the y - axis that shows the value of y.
• And you know very well, the values of x are known as zeros of polynomial.
• Hence, the number of intersection of graph of a polynomial on x - axis is the number of zeros of that polynomial.

Here We have a cubic polynomial. means, the power of polynomial is three. and the standard equation of polynomial would be P(x) = ax³ + bx² + cx + d, where a , b , c and d are real numbers.

We know, a cubic polynomial can have the maximum three zeros. so the polynomial cuts x - axis at almost three points.

Therefore the graph of a cubic polynomial cuts the x - axis at almost three points.

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