Question

For what value of 'k will the following quadratic equation:
k^2x^2–(k+1)x+ 9 = 0 have real and equal roots? ​

Answer 1

Step-by-step explanation:

The part under the root of the of the classic quadratic formula has to be positive for this and it is (−4k)2−4(k+1)(9)=16k2−4k−36

so

16k2−4k−36>0∣÷4

4k2−k−9>0

k<−(−1)−(−1)2−4(4)(−9)√2(4)=1−145√8≈−1.38∨k>−(−1)+(−1)2−4(4)(−9)√2(4)=1+145√8≈1.63

so

k∈(−∞,1−145√8)∪(1+145√8,∞)

hope it helps you