Show-that-the-graph-of-y-x-3-2x-2-x-1-between-x-1-and-x-2-lies-entirely-above-the-x-axis-

Question Number 11473 by tawa last updated on 26/Mar/17

Show that the graph of y = x^{3} + {2 x}^{2} + x + 1, between x = - 1 and x = 2

lies entirely above the x - axis

Commented by prakash jain last updated on 28/Mar/17

y = x^{3} + 2 x^{2} + x + 1

= x (x^{2} + 2 x + 1) + 1

= x {(x + 1)}^{2} + 1

y > 0 f o r x > 0

- 1 ⩽ x ⩽ 0

x {(x + 1)}^{2} > - 1

x {(x + 1)}^{2} + 1 > 0

Answered by sm3l2996 last updated on 26/Mar/17

Commented by tawa last updated on 26/Mar/17

God bless you sir .

Facebook Tweet Pin