Question

If 3p^2=5p+2 and 3q^2=5q+2 where p and q are distinct, obtain the equation whose roots are (3p-2q) and (3q-2p). ​

Answer 1

Answer:

3x² - 5x - 100 = 0

Step-by-step explanation:

We are given that p and q are both roots of the quadratic

3x² - 5x - 2 = 0.

So   p+q = 5/3   and   pq = -2/3.

Let α=3p-2q and β=3q-2p.  We need a quadratic with α and β as roots.

We have

α+β = (3p-2q) + (3q-2p) = p+q = 5/3

and

αβ = (3p-2q) (3q-2p)

    = 9pq - 6p² - 6q² + 4pq

    = 13pq - 6(p²+q²)

    = 25pq - 6(p²+2pq+q²)

    = 25pq - 6(p+q)²

    = 25 × (-2/3)  -  6 × (5/3)²

    = - 50/3  - 50/3

    = -100/3

So α and β are roots of

3x² - 5x - 100 = 0.

Answer 2

Answer:

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