Question

In the quadratic equation ax²+bx+c=0,if a=C then roots are​

Answer 1

Answer:

Hence, the roots of the quadratic equation ax2+bx+c=0 are real and distinct.

Step-by-step explanation:

know that the discriminant D of a quadratic equation ax 2 +bx+c=0 is:

D=b 2 −4ac

Since it is given that a and c are of opposite signs, therefore, we consider the following cases:

Case 1: If a>0 and c<0 then

ac<0⇒−ac>0

Therefore, we have:

D=b 2 −4ac=b 2 +4(−ac)=b 2

+4(−ac)>0(∵−ac>0)

⇒D>0

Case 2: If a<0 and c>0 then

ac<0⇒−ac>0

Therefore, as done in case 1:

D=b 2 −4ac>0

Hence, the roots of the quadratic equation ax

2

+bx+c=0 are real and distinct.