All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions.

(i)
$\frac{d}{dx} \mathrm{ln} (x^{2}+4)$

$= \frac{2x}{x^{2}+4}$

(ii)
$\frac{2x}{x^{2}+4} = k$

$kx^{2} - 2x +4k = 0$

(iii)
For $kx^{2} - 2x +4k = 0$ to have equal roots,

$Discriminant ~ = 0$

$(-2)^{2}-4(k)(4k) = 0$

$16k^{2}-4 = 0$

$(4k-2)(4k+2) = 0$

$k = \pm 0.5$

### KS Comments:

Question is well attempted and simple. Students just need to know the definition of discriminants well.

### One Comment

• […] Question 2 […]