Question

If 3p² = 5p +2 and 3q² = 5q +2
then the equation whose
roots 3p-2q and 39–2p is
O
x? – 5x +100 = 0
O
3x² – 5x –100 = 0
O
3x² + 5x +100 = 0
O
5x? – x + 7 = 0​

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.

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