Relation Between Zeroes (Roots) and Coefficients of a Quadratic Equation

Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients:

4s² – 4s + 1

For the following, find a quadratic polynomial whose sum and product respectively of the zeroes are as given. Also find the zeroes of these polynomials by factorisation.

`(-8)/3, 4/3`

Find the zeroes of the quadratic polynomial x² + 6x + 8 and verify the relationship between the zeroes and the coefficients.

If α, β, γ are the zeros of the polynomial f(x) = ax³ + bx² + cx + d, then α² + β² + γ² =

If 2 and -2 are two zeroes of the polynomial `(x^4 + x^3 – 34x^2 – 4x + 120)`, find all the zeroes of the given polynomial. 

If α and β are the zeros of the quadratic polynomial p(y) = 5y² − 7y + 1, find the value of `1/alpha+1/beta`

If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate `beta/(aalpha+b)+alpha/(abeta+b)`

Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients:

3x² – x – 4