Polynomials (C10)

Zeros of a polynomial. Relationship between zeros and coefficients of quadratic polynomials.

For what value of k, is the polynomial f(x) = 3x⁴ – 9x³ + x² + 15x + k completely divisible by 3x² – 5 ?

Find the zeroes of the quadratic polynomial 7y² – 11y/3 – 2/3 and verify the relationship between the zeroes and the coefficients.

Find all the zeroes of the polynomial 3x⁴ + 6x³ - 2x² - 10x - 5 if two of its zeroes are √(5/3) and – √(5/3)

Obtain all zeroes of 3x⁴ – 15x³ + 13x² + 25x – 30, if two of its zeroes are √5/3 and – √5/3

Find all zeroes of the polynomial (2x⁴ – 9x³ + 5x² + 3x – 1) if two of its zeroes are (2 + √3) and (2 – √3).

Find the zeroes of the quadratic polynomial x² + 7x + 10, and verify the relationship between the zeroes and the coefficients.