Question

If x=-5 and x=1/5 are solutions of the equation x^2 + kx+alpha =0 .Find the value of k and alpha

Answer 1

Let α and β be the roots of the equation x²+kx+p=0

Here x = -5 and 1/5

If α and β are the roots of the equation

then α+β = -b/a  and αβ = c/a

Here let α = -5  and β = 1/5

Here,

a = 1

b = k

c = p

Therefore -5+1/5 = -k/1 = -k

-24/25 = -k

∴ k = 24/25

-5×1/5 = p/1

-1 = p

∴ p = -1

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