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