Question
Question: If (t, 0) is a point on the diameter of the circle x<sup>2</sup> + y<sup>2</sup> = 4, then the equat...
If (t, 0) is a point on the diameter of the circle x2 + y2 = 4, then the equation x2 –4x –t2 = 0 has-
A
Distinct roots greater than 1
B
Exactly one real root in (–1, 0)
C
Both roots greater than 2
D
None of these
Answer
Distinct roots greater than 1
Explanation
Solution
Since (t, 0) is point on diameter of the circle given
\ max t2 = 4
Now say f(x) = x2 – 4x – t2
f(–1) > 0
f(2) < 0
f(0) Ј 0
f(5) > 0