# Zeros

Zeros, in mathematical terms, hold significant importance across various domains, from algebra to calculus and beyond. They represent the points at which functions intersect with the x-axis, indicating solutions to equations or the absence thereof. These critical points serve as anchors for understanding the behavior and properties of mathematical expressions, guiding analyses and problem-solving strategies. Whether in polynomial equations, complex functions, or digital systems, zeros stand as fundamental elements shaping mathematical models and practical applications. Understanding their characteristics and implications empowers mathematicians, scientists, and engineers to navigate complex systems and uncover deeper insights.

- How do you find all the zeros of #y=x^2-11x+30# with its multiplicities?
- What are all the zeroes of #f(x) = 2x^3 - 5x^2 + 3x - 1#?
- How do you find a polynomial function that has zeros 0, -3?
- How do you write a polynomial in standard form given the zeros x=1, -1, √3i, -√3i?
- How do you find all the zeros of #(3x^6+x^2-4)(x^3+6x+7)#?
- How do you solve #x^3+2x^2 = 2# ?
- How do you write a polynomial function of least degree and leading coefficient 1 when the zeros are 8, -i, i?
- How do you write a polynomial function of least degree and leading coefficient 1 when the zeros are 4, 4, 2+i?
- How do you write a polynomial function in standard form with zeros at 4, 5, and 2?
- How do you solve #x^4 – 8x^2 – 9 = 0#?
- What are the zeros of the polynomial function#f(x)=(x-3)(x-3)(x+5)#?
- How do you write a polynomial with zeros 1,-4, 5?
- How do you find all zeros of #f(x)=5x^4+15x^2+10#?
- How do you write a polynomial in standard form given zeros 8, -14, and 3 + 9i?
- What are the roots of #x^4-6x^3+14x^2-14x+5=0# with their multiplicities?
- The polynomial of degree 4, P(x) has a root multiplicity 2 at x=4 and roots multiplicity 1 at x=0 and x=-4 and it goes through the point (5, 18) how do you find a formula for p(x)?
- Given #M = ((1, 1, 1), (0, 5, 5), (0, 0, 7))#, is it true that there is a non-zero second degree polynomial of which #M# is a root?
- How do you find all the zeros of #F(X)= 3x^2 - 2x^2 + x +4#?
- The roots of the quadratic #2x^2+3x-1=0# are #alpha# and #beta#. Without calculating the roots, find #alpha^3+beta^3#?
- How do you write the polynomial function with the least degree and zeroes i, 2 - √3?