Question

Suppose $a,b,c$ are real numbers, and each of the equations $x^2+2ax+b^2=0$ and $x^2+2bx+c^2=0$ has two distinct real roots. then the equation $x^2+2cx+a^2=0$ has

• A. Two distinct positive real roots
• B. Two equal roots
• C. One positive and one negative root
• D. No real roots

Answer 1

Answer: (D)

No real roots

Now the equations have distinct real roots,

So $x^2+2ax+b^2=0a^2>b^2$ gives

And $x^2+2bx+c^2=0$ gives

$b^2>c^2$

from both we get $a^2>c^2$

Now for the equation $x^2+2cx+a^2=0$

we have $D=c^2-a^2<0$

So no real roots.

(D)