# Find the quadratic polynomial, the sum of whose zeros is \sqrt {2} and their product is -12. Hence, find the zeros of the polynomial.

2
by Rohs

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by Rohs

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we are given a+b=sqrt(2)

and

ab=-12

thus (a+b)^2= a^2+b^2+2ab

hence

2=a^2+b^2+2(-12)

so,26=a^2+b^2.............(1)

also (a-b)^2=a^2+b^2-2ab

= 26 - 2(-12)

=50

(a-b)=sqrt(50)...........(2)

solving (1) and (2)

a= (5sqrt(2)+sqrt(2))/2

b= (-5sqrt(2)+sqrt(2))/2

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