Question

Find a quadratic polynomial each with the given number as the sum and product of its zeros respectively

1/4 and 1​

Answer 1

The answer is 4x² – x – 4 = 0

Explanation:

1st Method

Given;

• Sum of zeroes = α + β = (-b)/a = 1/4
• Product of zeros = αβ = c/a = 1

Where,

• a = 4
• b = 1
• c = 4

So, one quadratic polynomial satisfying is given condition is 4x² – x – 4 = 0

2nd Method

Sum of zeroes = 1/4

Product of zeros = 1

Remember this formula

x² – (α + β)x + αβ

x² – 1/4x + 1

4x² – x – 4 = 0

Thus, The quadratic polynomial is

4x² – x – 4 = 0.