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So we know that for quadratic equation ax² +bx +c = 0 whose roots are m,n we know that x² - ( m + n)x +mn = 0 the previous quadratic equation we know sum of roots = -b/a product of roots = c/a so in this sum roots of the equation are 4x² +7x + 2 = 0 α +β = -7/4 αβ = 2/4 = 1/2 so to form the quadratic equation as given above using x² - ( m + n)x +mn = 0 so x² - ( α² + β² )x + (αβ)² = 0 so using formula a² +b² = (a +b)² - 2ab