Question

if alpha and beta are the roots of x^2+5x+a=0,and 2alpha+5beta=-1.then find the value of a.​

Answer 1

GIVEN :

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 ------(1)

2α + 5β = -1 -----(2)

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.