If the roots of the equation x2-2ax+a2+a-3 =0 are less than 3 then find the set of all possible values of a. (ans : -infinity, 2)
Given equation is:
x2 - 2ax + a2 + a - 3 = 0
⇒ x2 - 2ax + (a2 + a - 3) = 0
Let p and q be the roots of the given equation.
So, sum of roots = p +q = 2a and product of roots = (a2 + a - 3)
It is given that roots of equation are less than 3.
So, sum of roots < 6 (As 3 + 3 = 6)
2a < 6
⇒ a < 3
So, for any integral value of p and q less than 3, value of a is always less than 3.
Hence, the solution set of a will always be (2, -∞).