Question
Question: The value of k for which the equation 3x<sup>2</sup> + 2x (k<sup>2</sup> + 1) + (k<sup>2</sup> – 3k...
The value of k for which the equation
3x2 + 2x (k2 + 1) + (k2 – 3k + 2) = 0 has roots of opposite sign, lies in the interval:
A
(∞, 0)
B
(–∞, 1)
C
(1,2)
D
(3/2, 2
Answer
(1,2)
Explanation
Solution
As ax2 +bx+c = 0 has roots of opp. signs when
a > 0 , c < 0
so, k2 – 3k + 2 < 0 ⇒ (k – 1) (k – 2) < 0 or K ∈(1, 2)