KVPY SX SB Exam 2012 Question Paper

Question : 81 of 120

Marks: +1, -0

PART II

MATHEMATICS

Suppose a, b, c are real numbers, and each of the equations

x^2+2ax+b^2=0

and

x^2+2bx+c^2=0

has two distinct real roots. Then the equation

x^2 + 2cx + a^2 = 0

has

Solution:

\table x^2+2ax+b^2=0, x^2+2bx+c^2;D_1 > 0,D_2 > 0;4a^2+b^2 > 0,4b^2-4c^2 > 0;a^2 > b^2....(1),b^2 > c^2....(2)

From (1) and (2)

a^2 > b^2 > c^2

⇒a^2 > c^2⇒c^2-a^2 < 0

x^2+2cx+a^2=0

D=4c^2-4a^2 < 0

No real roots

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