Practicing Success
The least integral value of k for which $(k-2) x^2 + 8x + k +4≥0$ for all x ∈ R, is |
5 4 3 none of these |
4 |
We have, $(k-2) x^2 + 8x + k +4≥0$ for all x ∈ R for $(k-2)x^2+8x+k+4≥0$ discriminant ≤ 0 $⇒k-2>0$ 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. |