Question

find the quadratic polynomial with-1/4 as the sum and 1/4 as product of its zero​

Answer 1

standard form of quadratic polynomial = ax² + bx + c

given :-

sum of the quadratic polynomial = -1/4

product of the quadratic polynomial = 1/4

we know the relation between it's zeroes and coefficients.

sum of zeroes = -b/a

product of zeroes = c/a

let us compare now with the given sum and product of zeroes.

• -b/a = -1/4

minus and minus cancel.

we get, b/a = 1/4

• c/a = 1/4

now, both the denominators are equal. so no need to change anything.

therefore a = 4, b = 1 and c = 1

hence, the quadratic polynomial = 4x² + x + 1

Answer 2

Answer:

4x² +  x + 1  = 0

Step-by-step explanation:

Given Problem:

Find the quadratic polynomial with-1/4 as the sum and 1/4 as product of its zero​.

Solution:

To Find:

The quadratic polynomial.

----------------------

Method:

According to your question:

Sum of quadratic polynomial = -1/4

Product of the quadratic polynomial = 1/4

We know that,

Formula of quadratic equation:

x²-(Sum of root)x + (Product of root) = 0

Now,

Put the values in equation.

x² –(-1/4) x  + 1/4  = 0

Then  

Multiply by 4

We get ,

4x² +  x + 1  = 0 ................(ANSWER)