Question

If $a,b,c$ are in A.P., then the roots of the equation $a{x}^2+2bx+c=0$ are

• A. real and distinct
• B. real and equal
• C. real
• D. imaginary

Answer 1

The correct option is C real

$2b=a+c$ as $a,b,c$ are in A.P.

$D=b^2-4ac\Rightarrow (2b{)}^2-4ac.$

$D=4(b^2-ac)$

$=4\left(\right(\frac{a+c}{2}{)}^2-ac)$

$=4\frac{(a-c{)}^2}{4}=(a-c{)}^2>0$

$\therefore$ roots are real.