Question

!! ATTENTION!!!! Can you plzz solve sum no. 14. I mark him or her as brilliantlist. Tomorrow is my math's exam.​

Answer 1

Question - Determine 'm' so that the equation (4-m)x^2 + 2(m +2)x + (8m + 1) = 0 may have equal roots.

Solution - If roots are supposed to be equal then Discriminate has to be equal to 0

Therefore, we can say that --

$b {}^{2} - 4ac \: = 0$

Here, in the given equation, b = 2(m+2)

a = (4-m)

c = (8m + 1)

$(2(m + 2)) {}^{2} - 4(4 - m)(8m + 1) = 0 \\ \\ (2m + 4) {}^{2} + ( - 16 + 4m)(8m + 1) = 0 \\ \\ 4m {}^{2} + 16m + 16 - 128m - 16 + 32 {m}^{2} + 4m = 0 \\ \\ 36 {m}^{2} - 112m - 4m = 0 \\ \\ 36 {m}^{2} - 108m = 0$

$36m(m - 3) = 0 \\ \\ m(m - 3) = 0 \\ \\ m = \frac{0}{(m - 3)} \\ \\ m = 0 \\ or \\ m - 3 = \frac{0}{m} \\ \\ m - 3 = 0 \\ \\ m = 3$

So, values of m are 0 or 3

This means that If we put m = 0,3 then the given equation would have equal roots