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CAT 2003 Slot 1 — QA Question 29

Forming a Quadratic Equation and Relation between roots and coefficientsEasy
Passage / Data

Each question is followed by two statements, A and B. Answer each question using the following instructions

Choose 1 if the question can be answered by using one of the statements alone but not by using the other statement alone.
Choose 2 if the question can be answered by using either of the statements alone.
Choose 3 if the question can be answered by using both statements together but not by either statement alone.
Choose 4 if the question cannot be answered on the basis of the two statements.

Let p and q be the roots of the quadratic equation x2 − (α − 2)x − α − 1 = 0. What is the minimum possible value of p2 + q2?

Answer & solution

  • A

    0

  • B

    3

  • C

    4

  • 5

Solution

 p2 + q2 = (p + q)2 − 2pq                                 …(i)

 From given equation, p + q = α − 2 and pq = − α − 1

 Substituting values in equation (i), we get,

 p2 + q2 = α2 + 4 − 4α − 2(−α − 1)

= α2 + 4 − 4α + 2α + 2

= α2 − 2α + 1 + 5

= (α − 1)2 + 5

 Minimum value of p2 + q2 will be obtained by putting (α − 1) = 0

 ∴ Minimum value = 5

 Hence, option (d).

CAT 2003 Slot 1 QA Q29: Let p and q be the roots of the quadratic equation x 2 − (α − 2)x − α − 1 — Solution | TheCATExam