Question

find a quadratic polynomial each with the given numbers as the sum and product of the zeros respectievely -1/4,1/4

Answer 1

$\mathfrak{\huge{Hi !}}$

$\underline{\sf{Sum}}$ = $\tt{\frac{-1}{4}}$

$\underline{\sf{Product}}$ = $\tt{\frac{1}{4}}$

Polynomial = $\tt{x^{2} - (Sum)x + (Product)}$

=》 $\tt{x^{2} + \frac{1}{4} x + \frac{1}{4}}$

Multiply the equation by 4

=》 $\tt{4x^{2} + x + 1}$

Answer 2

Answer:

k{ 4x^2 + x +1 } = 0, where, 'k' is a constant

Step-by-step explanation:

Question ;

find a quadratic polynomial each with the given numbers as the sum and product of the zeros respectively -1/4,1/4

we are given sum and product of zeros

sum =  -1/4

product = 1/4

Also,

sum = -b/a

product = c/a

Thus, -b/a = -1/4

        c/a = 1/4

therefore ,

a = 4 ; b = 1 ; c = 1

standard form = ax^2 +bx + c = 0

Hence,the equation becomes k{ 4x^2 + x +1 } = 0

where, 'k' is a constant