Question

If α and β are zeroes of the quadratic polynomial x^2 + 5x + 2, find the value of:
1/ α + 1/β

Answer 1

ANSWER

f(x)=x

2

+5x+5

Comparingfromtheabovepolynomial

wegeta=1,b=5,c=5

So,Sumofzeros=α+β=

a

−b

=5

Productofzeros=αβ=

a

c

=5

valueofα

−1

+β

−1

=

α

1

+

β

1

=

αβ

β+α

=

5

−5

=1

Answer 2

Here is your answer

=x²-5x+4

=x²-x-4x+4

=x(x-1)-4(x-1)

=(x-4)(x-1)

x-4=0

x=4

α=4

x-1=0

x=1

β=1

THE ZEROES ARE 4 AND 1

=1/α+1/β-2αβ

=(1/4)+(1/1)-(2×4×1)

=(1/4)+1-8

=(1+4-32)/4

=(5-32)/4

=-27/4