if alpha and beta are the zeros of the polynomial 2x²+5x+k, find the value of k such that (alpha+beta)²- alpha*beta=24
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polynomial is 2x² +5x +k =0
α+β = -5/2
αβ = k/2
and (α+β)² - αβ = 24
⇒(-5/2)² -k/2 = 24
⇒25/4 - k/2 = 24
⇒(25-2k)= 24×4
⇒2k = 25-96 = -71
⇒k = -71/2
α+β = -5/2
αβ = k/2
and (α+β)² - αβ = 24
⇒(-5/2)² -k/2 = 24
⇒25/4 - k/2 = 24
⇒(25-2k)= 24×4
⇒2k = 25-96 = -71
⇒k = -71/2
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