Question

Find the quadratic poynomial the sun of whose zeroes is √2 and their product is
-1 .Hence find the zeroes of polynomial

Answer 1

Hello!

Let p be the sum of roots, q be the product of roots., then the quadratic polynomial formed is x²-px+q

here p=√2
q=-1

The quadratic polynomial formed is

x²-√2x-1

Let a,b be the roots

given a+b=√2

ab=-1

(a-b)²=(a+b)²-4ab
=√2²-4(-1)
=2+4
(a-b)²=6

a-b=√6

a+b=√2

a-b=√6

2a=√6+√2
a=√6+√2/2

a+b=√2

b=√2-(√6-√2/2)

=2√2-√6-√2/2
=√2-√6/2

Hence the zeroes of polynomial are √2+√6/2,√2-√6/2

hope helped!!!

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Answer 2

required quadratic polynomial =x²-(sum of zeros)x+(product of zeros)

x²-(√2)x-1

x²-√2x-1 is the required polynomial

let a,b be the roots

given a+b=√2..-------(1)
ab=-1

(a-b)²=(a+b)²-4ab

(a-b)²=6

a-b=√6 ----(2)


by solving (1) and (2) we get.

a=√2+√6/2 and b =√2-√6/2


I hope this will help u ;)