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

  • 18

alpha & beta are the roots of x2+5x+a=0

so alpha + beta= _ coefficient of x

  coefficient of x2

  = _ 5

  1

and alpha x beta = constant term

  coefficient of x2

  = a

  1

  • -6
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