If alpha and beta are zeros of a quadratic polynomial 2x^2+5x+k find the value of k such that (alpha+beta)^2-alpha.beta = 24
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2x² + 5x + k = 0 is the given quadratic equation and it is given that
(α+β)² - α.β = 24 ....(i)
As we know that,
α+β = -b/a = -5/2 ....(ii)
and α.β = c/a = k/2 ....(iii)
Putting values of (ii) & (iii) in (i) , we get
(-5/2)² - (k/2) = 24
=> 25/4 - k/2 = 24
=> (25-2k)/4 = 24
=> 25 - 2k = 96
=> 2k = 25 - 96
=> 2k = -7
=> k = -7/2
(α+β)² - α.β = 24 ....(i)
As we know that,
α+β = -b/a = -5/2 ....(ii)
and α.β = c/a = k/2 ....(iii)
Putting values of (ii) & (iii) in (i) , we get
(-5/2)² - (k/2) = 24
=> 25/4 - k/2 = 24
=> (25-2k)/4 = 24
=> 25 - 2k = 96
=> 2k = 25 - 96
=> 2k = -7
=> k = -7/2
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