Question

If αβis the zeros of 5x^2+5x+6=0 then [1+α] [1+β]=?​

Answer 1

α and β are the zeros of 5x²+5x+6

=> [1+α] [1+β]= 1+α+β+αβ

α+β = -b/a = -5/5 = -1

αβ = c/a = 6/5

=> 1+(α+β)+αβ

= 1+6/5 -1

= 6/5

Answer 2

Solution:

For the quadratic equation = ax^2 + bx + c = 0.

We know that,

Sum of roots = α + β = ( - b / a )

Product of roots = α•β = ( c / a )

Given equation = 5x^2 + 5x + 6 = 0

5x^2 + 5x + 6 = 0

α + β = ( - 5 / 5 ) = ( - 1)

α•β = ( 6 / 5 )

( 1 + α ) ( 1 + β ) = 1 + α + β + α•β = 1 + ( - 1 ) + 6 / 5

Therefore, ( 1 + α ) ( 1 + β ) = 6 / 5