Question

If alpha, beta are the zeroes of polynomial 25 p^2-15 p +12,then find the of alpha^-1 + beta^-1 + gamma^-1​

Answer 1

We have,

Polynomial 25p2−15p+2

On comparing that,

Ap2+Bp+C

Then,

A=25,B=−15,C=2

Given that,

Sum of roots

=α+β=A−B

α+β=2515

α+β=53

Product of roots

α.β=AC

α.β=252

Now,

2α1and2β1

Then,

Sum of roots

2α1+2β1=4αβ2α+2β

=24αβ(α+β)

=2αβ(α+β)=252×253=53×425=415

2α1+2β1=415

Product of roots

=2α1×2β1=4αβ1=254×21

=825

So, the equation of polynomial is

p2−(Sumofroots)p+productofroots

⇒p2−415p+825

⇒88p2−30p+25

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Hence, this is the answer.

Answer 2

$\huge\fbox\pink{✯Answer✯}$

$= 8x²-30x+25$

$\huge\boxed{\dag\sf\red{Thanks}\dag}$