Question

Find quadratic polynomial as sum and product of its zeroes of -1/4 , 1/4​

Answer 1

Answer:

The answer will be;

4x^2 - x + 1 = 0;

Step-by-step explanation:

Given;

sum of zeroes = -1/4;

product of zeroes = 1/4;

Let a (coefficient of x^2) be 1. (i)

Thus, sum of zeroes = -b/a;

-1/4 = -b/1;

b = 1/4; (ii)

Product of zeroes = c/a;

1/4 = c/1;

c = 1/4; (iii)

General form of a quadritic equation is;

ax^2 - bx + c = 0;

From statement (i) and equation (ii) and (iii);

= (1)x^2 - (1/4)x + (1/4) = 0;

= x^2 - x/4 + 1/4 = 0;

= (4x^2 - x + 1) / 4 = 0;

= 4x^2 - x + 1 = 0.

That's all.