Question

If the difference of the roots of the quadratic is 5and the difference of their cubes is 215.Find the quadratic equarion

Answer 1

Let the roots of the quadratic equation be 'α' and 'β'

So, according to the question....

⇒α-β = 5.......(1)

⇒α²-β² = 215........(2)

∴(1) gives ⇒ α = 5-β

Substituting 'α = 5-β' in (2)

⇒(5-β)²-β² = 215

⇒(5)²-10β+β²-β² = 215

⇒25-10β = 215

⇒-10β = 215-25

⇒β = 190/-10

⇒β = -19

∴ Substituting β = -19 in (1)

⇒α = 5+19

⇒α = 24

Now, using the formula to find the quadratic equation by the help of its roots

⇒x²-(α+β)x+αβ

⇒x²-(5)x+456

⇒x²-5x+456

∴x²-5x+456 is the required polynomial.