Verified answer

Answer:

[tex]x^{2} \\[/tex]- 8[tex]x[/tex]+ 12 = 0

Step-by-step explanation:

[tex]x^{2}[/tex]- ([tex]\alpha[/tex]+[tex]\beta[/tex])[tex]x[/tex] + [tex]\alpha \beta[/tex] = 0

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=x

2

−(8)x+12

Now , find the zeroes of the above polynomial.

Let f(x)=x

2

−(8)x+12

= x

2

−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 .