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Find the quadratic polynomial whose sum and product of zeroes are√2+1 and 1/√2+1

Posted by Sneha Vishnoi 4 years, 5 months ago

CBSE > Class 10 > Mathematics

3 answers

Amrit Raj 4 years, 5 months ago

Let the quadratic polynomial be =ax²+bx+c also, $ 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/a So we get a=1 b=-2√2 C=1 Hence the required polynomial is X²-2√2x+1=0 ans.

2Thank You

Adithya Dev A 4 years, 5 months ago

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]//

2Thank You

Sia ? 4 years, 5 months ago

2Thank You

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