Practicing Success
Practicing Success
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The least integral value of k for which $(k-2) x^2 + 8x + k +4≥0$ for all x ∈ R, is _____. |
| 4 |
We have, $(k-2) x^2 + 8x + k +4≥0$ for all x ∈ R $⇒k-2>0$ and $64-4 (k-2) (k + 4) ≤0$ $⇒k>2$ and $k^2 + 2k-24 ≥0$ $⇒k>2$ and $(k + 6) (k −4) ≥0$ $⇒k>2$ and $k ≤-6$ or, $k ≥4⇒ k ≥4$ Hence, the least integral value of k is 4. |
