Question

4a/9+1/3+13/108a=8a/18+19/18

Answer 1

Answer:

hello dear,

Step-by-step explanation:

Apply algebra. Here is the factor theorem.

The solutions of the polynomial are α and β.

→ There is (p-α)(p-β) as a factor.

25p²-15p+2=25(p-α)(p-β)

25p²-15p+2=25{p²-(α+β)p+αβ}

p²-3/5p+2/25=p²-(α+β)p+αβ

We have found that:

α+β=3/5

αβ=2/25

And this is called 'the relation between roots and coefficients'.

How do we construct such a polynomial? It is simple, just like we did before, we are gonna find sum and multiplication.

α/2 + β/2 = 3/10

αβ/4 = 1/50

And the polynomial is now p²-3/10p+1/50.

On making all numbers to integers, we get 50p²-15p+1.

i hope its helps u