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Find the quadratic polynomial whose sum and product of zeroes are√2+1 and 1/√2+1 |
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Answer» Let the quadratic polynomial be =ax²+bx+calso, $ and & are zeroes of given polynomial so, Since, $+&=-b/a =) √2+1+1/√2+1=-b/a =) 2√2=-b/a also, $•&=c/a =) √2+1×1/√2+1=c/a =) 1 =c/aSo we get a=1 b=-2√2 C=1Hence the required polynomial is X²-2√2x+1=0 ans. S = √2 + 1. P = 1/√2 + 1. Therefore, polynomial p(x) = k (x^2 - Sx + P) = k (x^2 - (√2 + 1)x + 1/√2 + 1 = k [(√2 + 1) x^2 - (3 + 2√2) x + 1]// |
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