Question

if a and B are zeroes of x^2-4x+1 then find the value of 1/a+2/B-aB​

Answer 1

Answer:

Correct option is

A

3

Given: α,β are zeroes of the polynomial x

2

−4x+1

To find the value of

α

1

+

β

1

−αβ

Sol: From the given quadratic equation,

α+β=4 and αβ=1

Therefore,

α

1

+

β

1

−αβ=

αβ

α+β

−αβ

⟹=4−1=3

Step-by-step explanation:

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Answer 2

Answer:

aB = 1

a + B = 4

1/a + 1/B = (a + B)/aB = 4/1 = 4

1/a+2/B-aB​ = (1/a+1/B)-aB​ + 1/B = 4 - 1 + (1/B)

D > 0

16 - 4 > 0 12 >0

a = 2 + root(3)

B = 2 - root(3)

(1/B) = 1/(2 - root(3)) rationalize it

2 + root(3) / 4 - 3

1/B = 2 + root(3)

1/a+2/B-aB​ = 3 + 2 + root(3)

5 + root (3)

hope it helps

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