Question

If a, b, c are in A.P, then the equation $(a-b)X^2+(c-a)X+(b-c)=0$ has two roots which are

• A. Real and unequal
• B. Real and equal
• C. Imaginary
• D. None of these

Answer 1

The correct option is B

Real and equal

If a,b,c are in A.P

b-a=c-b-------(1)
For the given quadratic equation, sum of coefficients = 0\)
$\Rightarrow$ 1 is a root(You can verify this by substituting 1 in the given equation)\)
$\Rightarrow$The other root, $\beta$ is $\frac{b-c}{a-b}[\beta X1=\frac{b-c}{a-b}]b-c=a-b$(from(1))
$\Rightarrow \beta =1$ or roots are real and equal