Question

A)if a and b are the zeros of the quadratic polynomial f(x)=x2-5x+4,find the value of 1/a+1/b-2ab.

B)write the zeros of the polynomial x2-2x+4.

Answer 1

A) f(x)=x2-5x+4
sum of root, a+b=-(-5)/1=5
product of root, ab=4/1=4
1/a+1/b-2ab=(a+b)/2b-2ab
putting the respective values of a+b,ab
we have
5/4-2*4
5/4-8
-27/8
B) Let f(x)=x2-2x+4
x2-2x+4=0
x2-2x=-4
Adding 1 to both side
we have
x2-2x+1=-4+1
(x-1)2=-3
Taking square root on both sides
we have
x-1=_+√3i
x=1+√3i or1-√3i

Answer 2

Answer:

A) f(x)=x2-5x+4

sum of root, a+b=-(-5)/1=5

product of root, ab=4/1=4

1/a+1/b-2ab=(a+b)/2b-2ab

putting the respective values of a+b,ab

we have

5/4-2*4

5/4-8

-27/8

B) Let f(x)=x2-2x+4

x2-2x+4=0

x2-2x=-4

Adding 1 to both side

we have

x2-2x+1=-4+1

(x-1)2=-3

Taking square root on both sides

we have

x-1=_+√3i

x=1+√3i or1-√3i