Question

If α and β are the zeros of the polynomial f(x) = x² + px + q, then a polynomial having 1/α and 1/β is its zeros is
A. x² + qx + p
B. x² – px + q
C. qx² + px + 1
D. px² + qx + 1

Answer 1

C. qx² + px + 1

Step-by-step explanation:

Given: Polynomial f(x) = x² + px + q

α and β are the zeroes of the polynominial.

Sum of zeroes = α+β = -b/a = -p

Product of zeroes = αβ = c/a = q

Given 1/α and 1/β are zero zeroes of polynomial f(x) = x² - Sx + P

So S =  1/α + 1/β  

= α + β / αβ

S = -p/q

P =  1/α * 1/β  

 = 1/αβ

P  = 1/q

Therefore the polynomial will be:

f(x) = x² +(p/q)x + (1/q)

 f(x)  = qx² +px + 1

Option C is the answer.

Answer 2

Answer

(C) qx²+px+1

Step by step explanation :-

the polynomial f(x)=x

2

−px+q has the roots as α and β.

Then the equation having the roots as

α

1

and

β

1

is f(

x

1

).

⇒ f(

x

1

)=(

x

2

1

)−p(

x

1

)+q

⇒ f(

x

1)=qx

2

−px+1.

Therefore the equation having

α

1

and

β

1

as roots is qx

2

−px+1.