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The maximum number of zeros of a Quadratic Polynomial is 

Learn about quadratic polynomials and their maximum zero count. Explore the fascinating world of mathematical functions.

by Maivizhi A

Updated Mar 06, 2024

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The maximum number of zeros of a Quadratic Polynomial is

The maximum number of zeros of a Quadratic Polynomial is 

The maximum number of real zeros of a quadratic polynomial is 2.

This is because a quadratic polynomial can be represented in the form:

ax^2 + bx + c

where a, b, and c are constants, and a ≠ 0.

Using the quadratic formula, we find the zeros of the polynomial:

x = (-b ± √(b^2 - 4ac)) / (2a)

Depending on the discriminant (b^2 - 4ac), there can be three different scenarios:

  1. If b^2 - 4ac > 0, there are two distinct real roots.
  2. If b^2 - 4ac = 0, there is one real root (a repeated root).
  3. If b^2 - 4ac < 0, there are no real roots (the roots are complex).

In all cases, the maximum number of real roots (zeros) is 2. This is a fundamental property of quadratic polynomials. 

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Zeros of Quadratic Polynomial 

The zeros of a quadratic polynomial ax^2 + bx + c can be found using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

where a, b, and c are the coefficients of the quadratic polynomial.

  1. If the discriminant b^2 - 4ac > 0, then the quadratic polynomial has two distinct real zeros.
  2. If the discriminant b^2 - 4ac = 0, then the quadratic polynomial has one real zero (the zeros are identical).
  3. If the discriminant b^2 - 4ac < 0, then the quadratic polynomial has two complex zeros.

The maximum number of zeros of a Quadratic Polynomial is - FAQs

1. What is the maximum number of zeros a quadratic polynomial can have?

The maximum number of zeros a quadratic polynomial can have is 2.

2. Why is the maximum number of real zeros for a quadratic polynomial 2?

The maximum number of real zeros for a quadratic polynomial is 2 because of its fundamental properties.

3. How do you find the zeros of a quadratic polynomial?

The zeros of a quadratic polynomial can be found using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a).

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