Polynomials

Define a polynomial and give an example of a linear polynomial in one variable.

Write the quadratic polynomial whose sum and product of zeroes are $-3$ and $2$ respectively.

Find the zeroes of the polynomial $p(x) = x^2 - 3$ and verify the relationship.

Find the value of the polynomial $5x - 4x^2 + 3$ at $x = -1$.

Can a quadratic polynomial have no zeroes? Explain with a graphical reference.

If $\alpha$ and $\beta$ are the zeroes of $2x^2 - 8x + 6$, find the value of $\alpha + \beta$ and $\alpha \beta$.

Find a quadratic polynomial whose zeroes are $2$ and $-3$.

If the product of zeroes of the quadratic polynomial $ax^2 - 6x - 6$ is 4, find the value of $a$.

Find the zeroes of the quadratic polynomial $f(x) = 6x^2 - 3 - 7x$ and verify the relationship between the zeroes and its coefficients.

Define a quadratic polynomial and state its general form with necessary conditions.

Explain the relationship between the zeros and the coefficients of a quadratic polynomial $ax^2 + bx + c$.

How can you form a quadratic polynomial if the sum and product of its zeros are given as $S$ and $P$ respectively?

Find the zeros of the quadratic polynomial $x^2 + 7x + 10$, and verify the relationship between the zeros and the coefficients.

Find the zeros of the quadratic polynomial $4u^2 + 8u$, and verify the relationship between the zeros and the coefficients.