Understanding a Quadratic Polynomial Whose Zeroes are 3 and 4

What is a Quadratic Polynomial?

A quadratic polynomial is a type of polynomial with two variables, usually expressed in the form ax² + bx + c. It is represented on a graph as a parabola, which is a curved “U” shape, with a vertex at the point where the curve changes direction. The most common uses of quadratic polynomials are to solve equations, calculate the area of a given shape, and to determine the turning points on a graph.

What Does it Mean When a Quadratic Polynomial has Zeroes of 3 and 4?

When a quadratic polynomial has zeroes of 3 and 4, it means that the equation has two solutions where the value of x is equal to 3 and 4. It is also possible to calculate the zeroes of a quadratic polynomial using the quadratic formula. The quadratic formula is used to calculate the solutions to a quadratic equation when the coefficients of the equation are known.

How to Calculate the Zeroes of a Quadratic Polynomial

The zeroes of a quadratic polynomial can be calculated using the quadratic formula. The quadratic formula is: x = (-b ± √b² – 4ac) / 2a. To use the formula, you need to know the coefficients of the equation. The coefficients are the values of a, b, and c in the equation ax² + bx + c. Once the coefficients are known, you can use the formula to calculate the zeroes of the equation.

How to Solve a Quadratic Polynomial Whose Zeroes are 3 and 4

Once the zeroes of a quadratic polynomial are known, it is possible to solve the equation. To solve a quadratic equation, you need to substitute the known zeroes into the equation and solve for the remaining unknown. To solve a quadratic equation whose zeroes are 3 and 4, you would substitute 3 and 4 into the equation, and then solve for the remaining unknown. For example, if the equation is x² + 2x + 5, you would substitute 3 and 4 into the equation and solve for the remaining unknown, which is 2. The solution to the equation would be 2.

Conclusion

A quadratic polynomial whose zeroes are 3 and 4 is an equation that has two solutions where the value of x is equal to 3 and 4. The zeroes of a quadratic polynomial can be calculated using the quadratic formula, and the equation can be solved by substituting the zeroes into the equation and solving for the remaining unknown. Knowing how to calculate and solve a quadratic polynomial whose zeroes are 3 and 4 can be an extremely useful skill, as it can be used to solve a variety of equations and problems.