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Question

Number of roots of a quadratic equation are:

A
1
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B
2
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C
3
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D
None
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Solution

The correct option is A 2

Let us, consider the quadratic equation of the general form

ax2+bx+c=0 where, a0

Now divide each term by a (Since a0), we get

x2 + bax+ca=0

x2+2b2ax + (b2a)2(b2a)2+ca = 0

After this we get

(x+b2a)2(b24ac2a)2=0

[x+(b2a)+(b24ac2a)][x+(b2a)(b24ac2a)]=0

[x((bb24ac2a))][x((b+b24ac2a))]=0

(xα)(xβ)=0,

where α=(bb24ac2a)

and β=(b+b24ac2a)

Now we can clearly see that the equation ax2+bx+c=0 reduces to
(xα)(xβ)=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)


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