Question

Find the quadratic polynomial sum of whose zeroes is 8 and their products is 12 find the zeroes of the polynomial

Answer 1

equation= x²-sx+px
=x²-8x+12
zeros= x²-6x-2x+12
=x(x-6)-2(x-6)=o
(x-2)(x-6)=o
x-2=o. x-6=o
x=2. x=6

so zero is 2and6

Answer 2

A polynomial is of the form ax²-bx²+c=0

given: sum of zeroes is 8

          product of zeroes is =12

a polynomial is formed as

x²-(α + β )+(α ×β)x =0

let the two zeroes be ∝ and β respectively

we know ,Sum of zeroes= $\frac{-b}{a}$ and product of zeroes =$\frac{c}{a}$

i.e α + β =8 and α×β = 12

putting value in the equation

x² - (8)x + 12=0

⇒ z² - 8x + 12 =0 is the polyonomial