Question

Hlo Brainliacs !

Maths Question :-

find the quadratic polynomial the sum of whose roots is √2 and product is 1/3. Also find the zeros of the polynomial.

Quick !!

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Answer 1

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Answer 2

Given

sum of roots= sqrt2

product of roots = 1/3

we know that

quadratic polynomial =k( x^2 - X(sum of roots of polynomial + product of roots of polynomial )

k(x^2 - sqrt2x + 1/3)

k/3(3x^2 - 3sqrt2 x+ 1)

so polynomial is

3x^2 - 3sqrt2x +1

now

a + b = sqrt2-----------(1

(a +b )^2 = 2

ab = 1/3

(a - b )^2 = 2 - 4/3 = 2/3 --------2

a - b = sqrt(2/3)

on adding ---1 and ----2

2a = (sqrt3 sqrt2+ sqrt2)/sqrt3

a =( sqrt3sqrt2 + sqrt2)/sqrt 3*2

b = 2b =2( sqrt3sqrt2 - sqrt2)/2*sqrt3