Please answer the Qs. 7 given above
Q.7. Find the greatest value of $3+5x-2x^2$ for all real values of x.

Let us assume y = 2x^2 - 3x + 5

Or, y = 2(x² - 3/2x) + 5

Or, y = 2(x² -2 * x * ¾ + 9/16 - 9/16) + 5

Or, y = 2(x - ¾)² - 9/8 + 5

Or, y = 2(x - ¾)² + 31/8

Hence, (x - ¾)² ≥ 0, [Since x ϵ R]

Again, from y = 2(x - ¾)² + 31/8 we can clearly see that y ≥ 31/8 and y = 31/8 when (x - ¾)² = 0 or, x = ¾

Therefore, when x is ¾ then the expression 2x^2 - 3x + 5 reaches the minimum value and the minimum value is 31/8.