Question

the equation px^2 - 22x + 8 =0 has two distinct roots a and b . also 1/a + 1/b = 9/4 . find p ​

Answer 1

Answer:

Given,a,b are distance roots of x

3

+3x

2

−1=0

⇒a

3

+3a

2

−1=0 and b

3

+3b

2

−1=0

let the third root be c

then c

3

+3c

2

−1=0

product of roots =

a

−d

=

1

−(−1)

=1

⇒

abc=1

c=

ab

1

but c is root of x

3

+3x

2

−1=0

⇒c

3

+3x

2

−1=0

⇒

(ab)

3

1

+

(ab)

2

3

−1=0

⇒

1+3ab−(ab)

3

=0

.....(1)

in equation (1)

(ab)

3

−3(ab)−1=0

⇒ab is root of

x

3

−3x−1=0

∴(ab) is root of

x

3

−3x−1=0

Answer 2

Answer:

p=5

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