Directions: Below question is followed by two statements labelled I and II. Decide if these statements are sufficient to conclusively answer the question. Choose the appropriate answer from the options given below: What is the value of C in this equation X2 + X + C = 0? I. the equation has one root II. the sum of the roots is -1

Directions: Below question is followed by two statements labelled I and II. Decide if these statements are sufficient to conclusively answer the question. Choose the appropriate answer from the options given below:

What is the value of C in this equation X² + X + C = 0?

I. the equation has one root

II. the sum of the roots is -1

A Statement I alone is sufficient to answer the question.

B Statement II alone is sufficient to answer the question.

C Statement I and Statement II together are sufficient, but neither of the two alone is sufficient to answer the question.

D Either Statement I or Statement I alone is sufficient to answer the question.

E Neither Statement I nor Statement II is sufficient to answer the question.

Solution

Correct Answer: Option A

X² + X + C = 0. Using the formula for the roots: \(\frac{{ - b \pm \sqrt {({b^2} - 4ac} }}{{2a}}\)

we have

\(\frac{{ - 1 \pm \sqrt {({1^2} - 4c} }}{2}\)

Given the equation has one root

\(\Rightarrow \sqrt {({1^2} - 4{\rm{c}}} = 0\)

⇒ c = ¼

Hence, statement I is sufficient to answer this question.

From statement II:

The sum of the roots is -b/a. This has got nothing to do with C.

Hence, statement II is not sufficient to answer this question.

Solution

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