Question

If $\alpha ,\beta$ are the roots of equation $(k+1)x^2-(20k+14)x+91k+40=0;(\alpha <\beta )$, $k>0$, then

The nature of the roots of this equation is

• A. imaginary
• B. real and distinct
• C. equal real roots
• D. None of these

Answer 1

The correct option is B real and distinct

Given equation is

$(k+1)x^2-(20k+14)x+91k+40=0$

$D=(20k+14{)}^2-4(k+1\left)\right(91k+40)=discriminant$

$\Rightarrow D=36(k^2+k+1)\ge 0$..........$(\because k^{2}andkarealwayspositiveforallk>0)$

$\because D>0$

$\therefore theequationhasrealroots$

Hence, option $B$ is correct.