Solve the following inequality: 2x^2 < x+3
2x2 < x+3, 2x2- x - 3 < 0, (2x - 3) (x + 1) < 0, Positive quadratic. Roots: x = -1 and x = 3/2, Therefore, x takes values greater than -1 and less than 3/2.
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Find roots 'a' and 'b' of the quadratic equation 2(x^2) + 6x + 7 = 0
'Find the first derivative, with respect to x, of arctan(1/x) for non-zero real x. Hence show that the value of arctan(x)+arctan(1/x) is constant for all non-zero x, explicitly stating this constant in your final answer.' How do I solve this?
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