if alpha and beta are the zeros of the polynomial kx ^2-5x+2 such that alpha-beta=2.find the value of k
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kx²-5x+2
∴α+β=5/k
∴αβ=2/k
given=α-β=2
=>(α-β)²=2²
=>α²+β-2αβ=4
=>(α+β)²-2ab-2ab=4
=>(5/k)²-4(2/k)=4
=>25/k²-8/k-4=0
=>4k²+8k-25=0
d =b²-4ac
=64+400=464
k=(-b+-√d)/2a
=(-8+-4√29)/8
=(√29 - 2)/2
or
=-(√29 +2)/2
∴α+β=5/k
∴αβ=2/k
given=α-β=2
=>(α-β)²=2²
=>α²+β-2αβ=4
=>(α+β)²-2ab-2ab=4
=>(5/k)²-4(2/k)=4
=>25/k²-8/k-4=0
=>4k²+8k-25=0
d =b²-4ac
=64+400=464
k=(-b+-√d)/2a
=(-8+-4√29)/8
=(√29 - 2)/2
or
=-(√29 +2)/2
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