What is a^2 + b^2 if a and b are the roots of x^2 + 3x - 4 = 0

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The roots of the equation x^2 + 3x - 4 = 0 are a and b.

x^2 + 3x - 4 = 0

= x^2 + 4x - x - 4 = 0

=> x(x + 4) - 1(x + 4) = 0

=> (x - 1)(x + 4) = 0

As the roots are x = 1 and x = -4, a = 1 and b = -4

a^2 + b^2 = 1^2 + (-4)^2 = 1 + 16 = 17

The value of a^2 + b^2 = 17

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