Find the quadratic polynomial whose zeroes are 2 + ✓3 and 2 – ✓3 .
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The zeros are 2+ 3 and 2− 3
Let the quadratic polynomial be (x−r1 )(x−r 2) where r1 and r2 are the zeros of the polynomial.
Thus the polynomial is
[x−(2+√3 )][x−(2−√3 )]
=(x−2− √3)(x−2+ √3)
=(x^2 −2x+ √3x−2x+4−2√3 − √3x+2√3−3)
=x^2 −4x+1
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