Question

Find the quadratic polynomial with zeroes 2 and

−1

3​

Answer 1

Answer:

The quadratic polynomial will be = (1/3)(3x^2–5x—2).

Step-by-step explanation:

• Let be quadratic polynomial be ax ^2  +bx +c and its zeroes be α and β

In our case ,α =2 and β = (-1/3)

• Sum of zeroes= α+β = 2 + (-1/3) = 2 - ( 1/3 )= (6–1)/3 =5/3

• Product of zeroes= αβ= 2*(-1/3)= -2/3

• The quadratic polynomial with the variable x :

=x^2- (sum of zeroes)x+ (product of zeroes)

=x^2- (5/3)x + (-2/3)

=(3x^2 - 5x -2)/3

=(1/3)(3x^2–5x—2)