Question

If α, β are the zeros of the polynomial 2y² + 7y + 5, write the value of α + β + αβ.

Answer 1

Let α and β are the zeros of the polynomial f(x) = 2y² + 7y + 5. Then

The sum of the zeros  = `(-text{Coefficient of y})/(text{Coefficient of }y^2) = (-7)/2`

The product of the zeros = `\text{Constant term}/\(text{Co-effecient of }y^2)=5/2`

Then the value of `α + β + αβ` is 

`α + β + αβ`

= `(-7)/2+5/2`

= `(-7+5)/2`

= `(-2)/2`

= `-1`

Hence, the value of `α + β + αβ` is –1.