Question

if a, b, c are real numbers such that AC ≠ 0 show that at least one of the equations x² + bx + c = 0 and -ax²+ bx + c = 0 has real roots.​

Answer 1

Step-by-step explanation:

Given {a,b,c}ϵR

and ac



=0

Let First eqn is ax

2

+bx+c=0

and other is −ax

2

+bx+c=0

and D

1

and D

2

are the discriminant of these eqn resp

Now, =D

1

=b

2

−4ac

D

2

=b

2

+4ac

case i)ac<0

then D

1

=b

2

−4ac>0

D

2

=b

2

−4ac→ cant say

case ii)ac>0

then D

1

=b

2

−4ac→ cant say

D

2

=b

2

+4ac>0

We can clearly observe that in both case atleast one equation have D>0 i.e. having real roots

Mark me as brainist please