Question

Write a quadratic polynomial, sum of whose zeroes is 6 and product is 12.​

Answer 1

ANSWER:-

Given: Sum fo zeroes = (α+β)=8

Product of the zeroes = αβ=12

Required quadratic polynomial is

x²−(α+β)x+αβ=x² −(8)x+12

Now , find the zeroes of the above polynomial.

Let f(x)=x² −(8)x+12

= x²−6x−2x+12

=(x−6)(x−2)

Substitute f(x)=0

(x−6)=0 or (x−2)=0

⇒x=6 or x=2

2 and 6 are the zeroes of the polynomial .

Answer 2

Step-by-step explanation:

let a and b are the zeroes of the quadratic polynomial

Then a+b = 6 and ab =12

Quadratic polynomial is always in the form of

x^2 - (a+b)x + ab

Now by putting the numbers, we get

x^2 -6x + 12

Hope this will help you and my explanation is good enough so you can understand

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