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Let a, b, c in R and a > 0. Consider th...

Let `a, b, c in R and a > 0`. Consider the statement If `b^2-4ac < 0`, then `ax^2 + bx +c lt 0 AA x in R`. Which of the following is equivalent to the negation of the above statement ?

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Let ax^2+bx+c=0, ane0 (a,b,c in R) has no real roots and a+b+2c=2 Statement-I: ax^2+bx+cgt0 forallx in R Statement II: a+b is positive.

Statement I If a gt 0 and b^(2)- 4ac lt 0 , then the value of the integral int(dx)/(ax^(2)+bx+c) will be of the type mu tan^(-1) . (x+A)/(B)+C , where A, B, C, mu are constants. Statement II If a gt 0, b^(2)- 4ac lt 0 , then ax^(2)+bx +C can be written as sum of two squares .

Statement I If a gt 0 and b^(2)- 4ac lt 0 , then the value of the integral int(dx)/(ax^(2)+bx+c) will be of the type mu tan^(-1) . (x+A)/(B)+C , where A, B, C, mu are constants. Statement II If a gt 0, b^(2)- 4ac lt 0 , then ax^(2)+bx +C can be written as sum of two squares .

Statement I If a gt 0 and b^(2)- 4ac lt 0 , then the value of the integral int(dx)/(ax^(2)+bx+c) will be of the type mu tan^(-1) . (x+A)/(B)+C , where A, B, C, mu are constants. Statement II If a gt 0, b^(2)- 4ac lt 0 , then ax^(2)+bx +C can be written as sum of two squares .