Question

Given that x

2+2kx+4k-3 = 0 has no real roots, show that k satisfies k
2
-4k+3 < 0

Answer 1

`{ \tt{2 + 2kx + 4k - 3 = 0}} \\ \\ { \tt{0 {x}^(2) + 2kx + (4k - 1) = 0 }}`

for unreal roots: b² < 4ac

• b is 2k

• a is 0

• c is 4k - 1

`{ \tt{ {(2k)}^(2) < (4 * 0 * 4k - 1)}} \\ \\ { \tt{4 {k}^(2) < 0 }} \\ \\ { \boxed{ \tt{k < 0}}}`