If alpha and beta are the roots of x2 +5x+a=0 and 2alpha +5beta= -1,then a is equal to
Given : α and β are the roots of the equation x2 + 5x + a = 0
⇒ α + β = -5/1 = -5
⇒ α = -β - 5 .....(1)
Also
2α + 5β = -1
Putting the value of α from (1) we get
2(-β - 5) + 5β = -1
⇒ -2β - 10 + 5β = -1
⇒ 3β = -1 + 10 = 9
⇒ β = 9/3 = 3
Putting the value of β in (1) we get
α = -3 - 5 = -8
Thus, αβ = a/1 = a
⇒ a = -8 × 3 = -24