Question

find a quadratic polynomial if the sum of zeros and product of zeros are 1 upon 4 and -1

Answer 1

Sum of roots = 1/4
Product of roots = -1

Quadratic equation -

x^2 -(Sum of roots)x + (Product of roots) = 0
x^2 - 1/4x+ (-1) = 0
4x^2 - x - 4 = 0

Hope This Helps You!

Answer 2

Given,
Sum of roots or zeroes =1/4
Product of roots or zeroes = -1

General form of a quadratic polynomial in variable x is x²-(Sum of roots)*x+Product of roots

⇒x²-(1/4)x-1

⇒x²-x/4-1

⇒4x²-x-4

∴ The Quadratic polynomial with sum of roots =1/4, Product of roots =-1 is x²-x/4-1 (or) 4x²-x-4