[3]
(b)
Calculate the values of c for which 2x2 – 3x + c>-2 for all values of x.

  c > -7/8

Step-by-step explanation:

Add 2 for an inequality that compares to zero:

  2x^2 -3x +(c+2) > 0

This will be true when the discriminant is negative. For the quadratic ...

  ax^2 +bx +c

the discriminant is ...

  b^ -4ac

We want this to be negative:

  (-3)^2 -4(2)(c+2) < 0

  9 -8(c +2) < 0

  9 -8c -16 < 0

  -7 < 8c

  -7/8 < c

The given inequality will be true for all values of c greater than -7/8.