If alpha and bita are the zeroes of kx2+4x+4 such that alpha sq. + beta sq.=24 find the values of k
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α and β are the roots of the given equation kx²+4x+4
Therefore, α+β = -4/k and αβ = 4/k
Using the identity, (α+β)² = α²+β²+2αβ
(-4/k)² = 24 + 2(4/k)
16/k² = 24+8/k. On cross-multiplying and simplifying, we get
24k²+8k-16=0
(taking 8 common) 8(3k²+k-2)=0
∴ 3k²+k-2 = 0
By splitting the middle term, we get (3k-2)(k+1) = 0
The two values of k are 2/3 and -1
PS: mark me as brainlist
Therefore, α+β = -4/k and αβ = 4/k
Using the identity, (α+β)² = α²+β²+2αβ
(-4/k)² = 24 + 2(4/k)
16/k² = 24+8/k. On cross-multiplying and simplifying, we get
24k²+8k-16=0
(taking 8 common) 8(3k²+k-2)=0
∴ 3k²+k-2 = 0
By splitting the middle term, we get (3k-2)(k+1) = 0
The two values of k are 2/3 and -1
PS: mark me as brainlist
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