Let a,b be non-zero real numbers Which of the following statements about the quadratic equation ax^2 +(a+b)x +b=0 is - Vedic Math - Simple Equations

Question

Let a,b be non-zero real numbers Which of the following statements
about the quadratic equation
ax^2 +(a+b)x +b=0 is necessarily true?
(I) It has atleast one negative root
(II) It has atleast one positive root
(III) Both its roots are real
A I and II only
B I amd III only
C II and III only
D All of them

Ishwarmani · Accepted Answer

Dear
Student,
Please find
below the solution to the asked query:

ax2+a+bx+b=0Here, D=a+b2-4ab=a2+b2+2ab-4ab=a2+b2-2ab=a-b2≥0⇒D≥0i
e
 both roots are realSo, x=-a+b±a-b22a=-a+b±a-b2a⇒x=-a+b-a-b2a or x=-a+b+a-b2a⇒x=-2a2a or x=-2b2a⇒x=-1 or x=-ba⇒Atleast one root is negativeHence, the correct option is B

Hope
this
information will clear
your doubts about the
topic
Regards