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If = x 0+ ( e x - e x x - x ) and = x 0(1 + x) 12 x are the roots of the quadratic equation ax2 + bx - e = 0, then 12 e(a + b) is equal to .
6
Let u = x, v = x (u, v 0):
= ev eu - v - 1u - v = 1 1 = 1
is a 1 form: = eL, where L = x 0 x 12 x = x 0 x2 = 12
So = e1/2 = e
Product of roots: 1 e = - ea a = -1
Sum of roots: 1 + e = - ba = b ⇒ a + b = e
∴ 12 e e = 12 12 = 6
Answer: 6
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