Relationship between Zeroes and Coefficients of a Polynomial

The product of zeroes of $3x^3-5x^2-11x-3$

If $\alpha , \beta$ are the roots of $a{x}^2+bx+c=0$, then ${\left(\frac{\alpha }{a\beta +b}\right)}^3-{\left(\frac{\beta }{a\alpha +b}\right)}^3=$

$\alpha , -\frac{3}{2}$ are the zeroes of $x^2+\frac{1}{6}x-2$, then find the value of $\alpha$

Find the sum and product of the zeroes of the polynomial: $f\left(x\right)=x^2-3x-10$

Prashant claims that the polynomial $p\left(x\right) = m{x}^n+x^{2b}\left(a>2b\right)$  has $4b$ zeroes. For Prashant's claim to be correct. which of these must be true?

Ankita got an electric wire and she wanted to bend the wire in a mathematical shape. She bent the wire in a shape of a parabola. A parabola has one of the two shapes either open upwards like $\cup$or open downwards like $\cap$. The shape made by Ankita is shown in the below figure:

The sum and product of a quadratic polynomials are $-1$ and $-6$ respectively, then the zeroes of the polynomial are

If the zeroes of quadratic polynomial $a{x}^2+bx+c$ are reciprocal to each other than the relationship between $c$ and $a$ is

If $\alpha$ and $\beta$ are zeroes of quadratic polynomial $f\left(x\right)=x^2-px+q,$ then find the value of $\frac{1}{\alpha }+\frac{1}{\beta }$.

If $\alpha$, $\beta$ are the zeroes of the polynomial $p\left(x\right)=3x^2-2x-6$, then find $\frac{1}{\alpha }+\frac{1}{\beta }$.

If the product of the zeros of the polynomial $a{x}^2-5x+6$ is $5$, then find the value of $a$.

If one zero of the polynomial $x^3-2x^2+x+5$ is zero, then find the product of other two zeroes.

If $\alpha$ and $\beta$ are the zeroes of the quadratic polynomial $f\left(x\right)=a{x}^2+bx+c$, then evaluate ${\alpha }^2\beta +\alpha {\beta }^2$. If ${\alpha }^2\beta +\alpha {\beta }^2=\frac{k}{a^2}$ then, write the value of $k$ as final answer.

If the zeroes of the polynomial $x^2+px+q$ are double in value to the zeroes of $2x^2-5x-3$, then find the value of $p-q$.

The zeroes of the quadratic polynomial $x^2+kx+k, k\ne 0$,

If one zero of the polynomial $p\left(x\right)=x^2-6x+k$ is twice the other then find the value of $k.$

A quadratic polynomial whose zeroes are $5$ and $-3$ is

If α , β are the zeroes of a polynomial, such that α + β = 6 and αβ = 4, then what is the polynomial equation?

The product of zeroes of the polynomial, ax² + bx + c, is given by

The sum of zeroes of the polynomial, ax² + bx + c, is given by

 Form the quadratic polynomial in t, whose roots are  2 + √ 5 and 2 - √ 5