Question

Suppose we have a quadratic equation ax²+bx+c=0 so that a+c=0.Does the quadratic equation have one solution or two distinct solutions? Are they real or complex? Explain how you know.

Answer 1

Answer:

The roots of equation are real and distinct.

Step-by-step explanation:

Given that

ax²+bx+c=0

a+c=0

To find the behavior of roots we have to find out D

$D=\sqrt{b^2-4ac}$

If

D> 0  Two real distinct roots

D=0  Two equal roots

D<0 Tow imaginary  roots

$D=\sqrt{b^2-4ac}$

a+c=0

a= - c

$D=\sqrt{b^2-4\times (-c)\times c}$

$D=\sqrt{b^2+4\times c^2}$

It means that D>0 .So the roots of equation is real and distinct.