If a and b are real and a ≠ b then show that the roots of the equation (a−b)x2+5(a+b)x−2(a−b)=0 are real and unequal.
The given equation is (a−b)x2+5(a+b)x−2(a−b)=0
Given, a, b are real and a≠b.
Then, Discriminant (D) =b2–4ac
We know that the square of any integer is always positive that is, greater than zero.
Hence, (D) =b2–4ac≥0
As given, a, b are real and a≠b.
Therefore, the roots of this equation are real and unequal.