Question

find a quadratic equation having sum and product of the roots as 1/ 4

Answer 1

x^2 + 1/4x + 1/4 is derived by this quadratic equation ax^2 +x[a+b]+ab =0

Answer 2

Answer:

4x² - x + 1 = 0

Step-by-step explanation:

We know that every Quadratic Equation is of form

k [ x² - ( sum of roots) x + (product of roots)], where k is any constant value

Now sum of roots = 1/4 and product of roots = 1/4

∴ k [ x² - (1/4)x + (1/4)] = 0

considering k = 4               [ LCM of Denominators is 4]

4 [ x² - (1/4)x + (1/4)] = 0

4x² - x + 1 = 0

Hence desired quadratic equation is 4x² - x + 1 = 0