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Roots are a and b p(x)=2x²+5x+k α+β= - b/a so, a+b= - b/a = - 5/2 αβ=c/c so, ab=c/a = k/2 given that, (a+b)²-ab=24 so, ( - 5/2)²-k/2 = 24 25/4 -k/2 = 24 25-2k/4=24 25-2k=24×4 -2k=96-25 k=71/-2 k= -35.5

P(x) = 2x^2 + 5x + k compair with Ax^2 + Bx + C A = 2, B = 5, C = k if roots of the equation is a and b then , a + b = -B/A = -5/2 ab = C/A = k/2 given (a + b)^2 - ab = 24 putting the value of a +b and ab (-5/2)^2 - k/2 = 24 25/4 - k/2 = 24 -71/4 = k/2 k = -71/2