Maths Problems. Help Please !?
1a) Prove that Sin3x + Sinx = (4Sinx)(Cos^2x)
1b) Find all the angles between 0 and π ( pie ) which satisfy the equation Sin3x + Sinx = 2cos^2x
2a) Find the smallest value of the integer a for which ax^2 + 5x + 2 is positive for all values of x.
2b) Find the smallest value of the integer b for which -5x^2 + bx - 2 is negative for all values of x.
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(1) Is a straight-forward routine homework problem, so I will not comment unless you show your work.
(2) Is wrong. There is no smallest "a" making the given expression positive for all "x". There is a smallest "a" making the expression non-negative. Use the discriminant. (Look that up in your notes.)
Similarly, there is no smallest "b" making the given expression negative. There is a smallest "b" making the expression non-positive. There is also a largest "b" in that case.