Number of roots of a quadratic equation are:
Let us, consider the quadratic equation of the general form
ax2+bx+c=0 where, a≠0
Now divide each term by a (Since a≠0), we get
⇒ x2 + bax+ca=0
⇒ x2+2b2ax + (b2a)2−(b2a)2+ca = 0
After this we get
⇒ (x+b2a)2 – (√b2−4ac2a)2=0
⇒ [x+(b2a)+(√b2−4ac2a)][x+(b2a)−(√b2−4ac2a)]=0
⇒ [x−((−b−√b2−4ac2a))][x−((−b+√b2−4ac2a))]=0
⇒ (x−α)(x−β)=0,
where α=(−b−√b2−4ac2a)
and β=(−b+√b2−4ac2a)
Now we can clearly see that the equation ax2+bx+c=0 reduces to
(x−α)(x−β)=0 and the equation ax2+bx+c=0 is only satisfied
by the values x=α and x=β.
Except α and β no other values of x satisfies the equation
ax2+bx+c=0
Hence, we can say that the equation ax2+bx+c=0 has only two roots.
Therefore, number of roots of Quadratic Equation are 2
Hence Answer is (B)