Question

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

Answer 1

Answer:

Given,

f(x)=ax

2

+bx+c

g(x)=bx

2

+cx+a

If we set t as the common root, then we know that f(t)=g(t)=0:

at

2

+bt+c=bt

2

+ct+a

We can equate coefficents to conclude that a=b=c

Therefore, we can say that

abc

a

3

+b

3

+c

3

=

aaa

a

3

+a

3

+a

3

=

a

3

3a

3

=3

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