Question

find the quadratic polyonomial sum of whose zeroes is 8 and their productis 12
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Answer 1

Step-by-step explanation:

Given: Sum fo zeroes = (α+β)=8

Product of the zeroes = αβ=12

Required quadratic polynomial is

x 2−(α+β)x+αβ=x2−(8)x+12

Now , find the zeroes of the above polynomial.

Let f(x)=x 2−(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

Answer 2

Answer:

x² - 8x + 12

Step-by-step explanation:

Product of roots ---> 12

Sum of roots ---> 8

We know that when we are given the sum and of products of roots, a quadratic equation can be written as:

x² - (Sum of roots)x + (Product of roots)

=> x² - (8)x + (12)

=> x² - 8x + 12 is our required equation.