If zeros of polynomial 6x 2 +4x+2a are α and 1/a , then find the value of a.
Answers
Answered by
2
p(x) = 6x^2 + x - 2
To find the zeros, let p(x) = 0
6x^2 + x - 2 = 0
x^2 + (1/6)x - 1/3 = 0
(x + 1/12)^2 - 1/144 - 48/144 = 0
(x + 1/12)^2 - 49/144 = 0
(x + 1/12)^2 - (7/12)^2 = 0
(x + 1/12 + 7/12)(x + 1/12 - 7/12) = 0
(x + 2/3)(x - 1/2) = 0
x = -2/3 or x = 1/2
Let α = -2/3 and β = 1/2
α/β+ β/α
= (-2/3) / (1/12) + (1/12) / (-2/3)
= -24/3 - 3/24
= -8 - 1/8
= -65/8
To find the zeros, let p(x) = 0
6x^2 + x - 2 = 0
x^2 + (1/6)x - 1/3 = 0
(x + 1/12)^2 - 1/144 - 48/144 = 0
(x + 1/12)^2 - 49/144 = 0
(x + 1/12)^2 - (7/12)^2 = 0
(x + 1/12 + 7/12)(x + 1/12 - 7/12) = 0
(x + 2/3)(x - 1/2) = 0
x = -2/3 or x = 1/2
Let α = -2/3 and β = 1/2
α/β+ β/α
= (-2/3) / (1/12) + (1/12) / (-2/3)
= -24/3 - 3/24
= -8 - 1/8
= -65/8
Similar questions