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If α and β are the zeros of polynomial P(x) =x^2-5x+k and α-β=1, then find k

[Hint:(α+β)^2=(α-β)^2+4αβ]

2
by prituldave

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[Hint:(α+β)^2=(α-β)^2+4αβ]

by prituldave

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The Brainliest Answer!

therefore p(x) = (x-α)(x-β)

x^2-5x+k = (x-α)(x-β)

x^2-5x+k = x^2-(α+β)x+αβ

equating the coefficients of x on both sides we get,

α+β = 5....(1)

equating the constants on both sides we get αβ = k ...(2)

We have α-β = 1 .....(3)

Solving (1) and (3) we get α=3 and β = 2

therefore k = αβ

=3*2

= 6

alpha*beta=k (Sum of roots=-b/a,prod. of roots=c/a for ax^2+bx+c=0)

from the given hint,

(5^2)=(1^2)+4k

25=1+4k

24=4k

=>k=6