Question

in quadratic equations ax^2+bx+c=0 if a and c are opposite signs and b is real, then the roots of the equation are

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Answer 1

Answer:

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Answer 2

We know that the discriminant D of a quadratic equation ax2 +bx+c=0 is:

⇒D=b2−4ac

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

⇒D=b2 −4ac= b2 +4(−ac)= b2 +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=b2 −4ac>0

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