Question

Find a quadratic polynomial whose sum and product of zeros are 1/3 and -1/3.

Answer 1

Step-by-step explanation:

let zeroes be A and B

So the sum of zeroes is 1/3

A+B=1/3=-b/a

so b=-1 and a =3

A*B =-1/3=c/a

so c=-1

so the quadratic equation is

ax²+bx+c

by substituting a,b,c

3x²-x-1

Thank you

Regards

Answer 2

Quadratic polynomial whose sum and product of zeros are 1/3 and -1/3 is 3x² -x -1

Step-by-step explanation:

The zeros of a polynomial are the ones values of the variable for which the polynomial as an entire has 0 value. The sum and manufactured from zeros in a quadratic polynomial have an immediate relation with the coefficients of variables withinside the polynomial.

If α and β are the zeros of the quadratic polynomial f(x): ax2+bx+c, the sum of the roots of the polynomial is: α+β= −b/a. In different words, it refers to (-coefficient of x)/ (coefficient of x2).

If α and β are the zeros of the quadratic polynomial f(x): ax2+bx+c, the manufactured from the roots of the polynomial is: αβ= c/a.

In different words, it refers to (consistent term)/ (coefficient of x2).

The sum of zeroes are 1/2

X + Y = ⅓ = -B/A

Hence ,

B = -1

A = 3

The product of Zeroes are

X × Y= -⅓ = C/A

C = -1

So ,

Equation= ax²+bx+c

= 3x² -x -1

(#SPJ2)