Question

write the polynomial whose zeros are -2-√3&2-√3​

Answer 1

Solution:

Let m,n are two zeroes of the

polynomial,

m = -2-√3, n = 2-√3

i) m+n = -2-√3+2-√3

=-2√3

ii) mn = (-2-√3)(2-√3)

= -(2+√3)(2-√3)

= -[2²-(√3)²]

= -(4-3)

= -1

Now ,

Form of a polynomial whose zeroes are m, n is

k[x²-(m+n)x+mn]

= k[x²-(-2√3)x+(-1)]

= k[x²+2√3x-1]

It is true for all real values of k.

If k=1 ,

Required polynomial is

= x²+2√3x-1

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