Hi
for a quadratic equation \(ax^2+bx+c=0\)..
SUM of roots = \(-\frac{b}{a}\)and PRODUCT of roots =\(\frac{c}{a}\)..
here a is 1, so we just require 'c'..

statement II gives us value of 'c'..
hence suff
B
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We are given that the quadratic equation x^2 + bx + c = 0 has two different roots. We need to determine the product of these two roots.

Recall that in a quadratic equation in the form ax^2 + bx + c = 0, the sum of the two roots is –b/a and the product of the two roots is c/a. Here, we are given the equation in the form of x^2 + bx + c = 0, and since a = 1, the product of the two roots is c/1 = c.

Thus, if we know the value of c, then we know the product of the two roots.

Statement One Alone:

One of the roots is 3.

We are given that one of the roots is 3. However, since we don’t know the value of the other root, we can’t determine the product of the two roots. Statement one alone is not sufficient. Eliminate choices A and D.

Statement Two Alone:

c = 6

Since we know the value of c, the product of the two roots must be 6 (see problem stem analysis above). Statement two alone is sufficient.

Answer: B
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Could someone please tell me if my approach is correct?


If \(x^2 + bx +c = 0\)
Then, (x + p)(x + q) = 0

Therefore
pq = c
p + q = b

The roots of the quadratic equation will be -p and -q.
The question is asking about the product of the roots, meaning (-p)(-q) = ?
This is equal to c = ?, which in turn is equal to pq = ?

- Statement 1: Insufficient, since it only provides -p = 3 or -q = 3
- Statement 2: Sufficient.

OA = B
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For a quadratic equation, \(ax^2+bx+c=0\)
If we have two roots x1 and x2,
x1+x2 = \(-\frac{b}{a}\) and x1*x2 = \(\frac{c}{a}\)

We have been asked to find the value of x1*x2.
Given data: quadratic equation in hand that a=1

Coming to the statements :
1) One of the roots is 3.
Knowing one of the roots is not going to be enough, as the other root
can be any number and therefore, the product of the roots will be
different for every different value of the second root(Insufficient)
2) c=6
If a=1, the product of the roots is also c which is 6(Sufficient)(Option B)

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