Question

Hii !

Solve this problem given in the attachment .

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Answer 1

Answer:

(d)

Step-by-step explanation:

alpha = a ; beta = b

from the eqn.....

a + b = - q/p. ; a × b = r/p

since...p, q, r are in AP.....

2q = p + r............,.(1)

now...1/a + 1/b = ( a + b ) / ab = 4

means....(-q/p) / (r/p) = 4

-q/r = 4 ; q = -4r..............(2)

from (1) & (2).....

2(-4r) = p + r

9r = - p

now....| (a - b )| = | √ [( a + b )^2 - 4 a b] |

| (a - b )| = | √ [ (-q/p)^2 - 4r/p ] |

= √ ( q^2 - 4rp ) /p

= √( 16r^2 + 36r^2) / 9r ( using (1) & (2) also | | )

= 2 √13r / 9r

= 2 √13 / 9

Answer 2

$\huge\mathtt\purple{Answer:-}$

$\implies\sf$Answer:

(d)

Step-by-step explanation:

alpha = a ; beta = b

from the eqn.....

a + b = - q/p. ; a × b = r/p

since...p, q, r are in AP.....

2q = p + r............,.(1)

now...1/a + 1/b = ( a + b ) / ab = 4

means....(-q/p) / (r/p) = 4

-q/r = 4 ; q = -4r..............(2)

from (1) & (2).....

2(-4r) = p + r

9r = - p

now....| (a - b )| = | √ [( a + b )^2 - 4 a b] |

| (a - b )| = | √ [ (-q/p)^2 - 4r/p ] |

= √ ( q^2 - 4rp ) /p

= √( 16r^2 + 36r^2) / 9r ( using (1) & (2) also | | )

= 2 √13r / 9r

= 2 √13 / 9

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