Question:
If one root of the equation x2 – kx + k = 0 exceeds the other by 23 then which one of the following is a value of k?
If one root of the equation x2 – kx + k = 0 exceeds the other by 23 then which one of the following is a value of k?
Options:
- a) 3
- b) 6
- c) 9
- d) 12
- a) 3
- b) 6
- c) 9
- d) 12
correct answer : b)
Explanation:
Here, a + b = k, ab = k
and a – b = 23()
\ (a – b)2 = (a + b)2 – 4ab
Þ 23
2
() = k2 – 4k
Þ k2 – 4k – 12 = 0 Þ k2 – 6k + 2k – 12 = 0
Þ (k – 6) (k + 2) = 0 Þ k = -2, 6
Here, a + b = k, ab = k
and a – b = 23()
\ (a – b)2 = (a + b)2 – 4ab
Þ 23
2
() = k2 – 4k
Þ k2 – 4k – 12 = 0 Þ k2 – 6k + 2k – 12 = 0
Þ (k – 6) (k + 2) = 0 Þ k = -2, 6