Question

Find for what real values of 'x', the
following expressions are positive or negative
a) x² - 2x - 3. b) 2x² + 5x – 3.

please answer my question​

Answer 1

Answer:

wait I am finding wait

I am trying

Answer 2

Answer:

The given function is [(x+2)/ (2x2 + 3x + 6)]

Clearly, the function (2x2 + 3x + 6) is a quadratic function with a = 2 > 0 and so it will have its minimum at x = –b/2a = –3/4 and minimum value is

–D/4a = 9-48/ 4.2 = 39/8

Moreover, D < 0 & 2x2 + 3x + 6 > 0 ∀ x

Hence, 0 < 1/ (2x2 + 3x + 6) < 8/39 ∀ x ∈ R

Hence, [(x+2)/ (2x2 + 3x + 6)] will have its maximum at x = –3/4

And the maximum value is given by (-3/4 + 2)/ (39/8) = 10/3