Question

In the quadratic equation ax"+bx+cOla,b,cec) a 20.
If 'a' and 'c' are of the same signs, then the product of
the roots (c/a) is​

Answer 1

Answer:

Step-by-step explanation:

We 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.