Question

Let f(x) be a quadratic polynomial satisfying f(2) +f(4) = 0.
If unity is one root of f(x) = 0 then find the other root.​

Answer 1

Answer:

Let 1 and

2

7

are roots of f(x)=0

So, sum of roots =1+

2

7

=

2

9

Product of roots =(1)

2

7

=

2

7

So, the quadratic equation is

x

2

−

2

9

x+

2

7

=0

Also, f(2)=−

2

3

f(4)=

2

3

Here, f(2)+f(4)=0

Hence, our assumption is correct.

2

7

is a root of f(x)=0

Now,if f(x)=ax

2

+bx+c

Let α,β are the roots of f(x)

Then, sum of roots =α+β=−

a

b

& product of roots =αβ=

a

c

.