If alpha , beta are roots of x²+5x+a=0 and 2alpha + 5beta =-1, then find the value of alpha and beta
Answers
Answered by
7
quadratic polynomial : x² + 5x + a = 0
zeroes of polynomial = α and β
we know that,
sum of zeroes using coefficients :
= α + β
= -b/a
= -5/1
α + β = -5
α = -5 - β )
2α + 5β = -1 )
substitute eq - (1) in eq -(2)
2(-5 - β) + 5β = -1
-10 - 2β + 5β = -1
-10 + 3β = -1
3β = -1 + 10
3β = 9
β = 3
substitute β in eq - (2)
2α + 5β = -1
2α + 5(3) = -1
2α + 15 = -1
2α = -1 - 15
2α = -16
α = -16/2
α = -8
we know that,
product of zeroes = c/a
= αβ
= 3(-8)
= -24
therefore, the value of a is -24.
Answered by
3
Answer:
Step-by-step explanation:
Attachments:
Similar questions