Question

If A and B are zeros of the quadratic polynomial x- 2x - 1, find a polynomial which roots are
i) 1/A + 1/B
2)A^2/B B^2/A
​

Answer 1

Answer:

1

Step-by-step explanation:

f(x)=x

2

−x−2

a=1

b=−1

c=−2

D=b

2

−4ac=(−1)

2

−4×1×(−2)=1+8=9

∵α and β are the zeroes of above polynomial.

∴ Sum of roots =

a

−b

⇒α+β=−

1

−1

⇒α+β=1⟶(1)

Difference of roots =

a

D

⇒∣β−α∣=

1

9

=3

Product of roots =

a

c

⇒αβ=

1

−2

⇒αβ=−2⟶(2)

∴

α

1

−

β

1

=

αβ

∣β−α∣

From eq

n

(1)&(2), we have

⇒

α

1

−

β

1

=

−2

3

=−

2

3

Or

Simply find the roots of given equation & hence solve.

Hence, (A) is the correct answer