Question

If alpha , beta are roots of x²+5x+a=0 and 2alpha + 5beta =-1, then find the value of alpha and beta

Answer 1

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.

Answer 2

Answer:

Step-by-step explanation: