Question

If a+ß are zeroes of polynomial p(x)=x²-5x+6,then find the value of
a+ß= 3aß.​

Answer 1

EXPLANATION.

α and β are the zeroes of polynomial.

⇒ P(x) = x² - 5x + 6.

As we know that,

Sum of the zeroes of the quadratic polynomial.

⇒ α + β = -b/a.

⇒ α + β = -(-5)/(1).

⇒ α + β = 5. - - - - - (1).

Products of the zeroes of the quadratic polynomial.

⇒ αβ = c/a.

⇒ αβ = 6. - - - - - (2).

To find : α + β = 3αβ.

As we know that,

Put the value of equation (1) and equation (2), we get.

⇒ α + β = 3αβ.

⇒ α + β - 3αβ = 5 - 3(6).

⇒ α + β - 3αβ = 5 - 18.

⇒ α + β - 3αβ = - 13.

Value of : α + β = 3αβ is - 13.