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The roots of ax2 + bx + c = 0 : GATE 2014-Paper 1

The roots of ax2 + bx + c = 0 : GATE 2014 – Paper 1

The roots of ax2 + bx + c = 0 are real and positive a, b, and c are real. Then ax2 + b|x| + c = 0 has

(A) No roots
(B) 2 real roots
(C) 3 real roots
(D) 4 real roots

Answer

ax2 + bx + c = 0, for roots to be real & +ve b2 − 4ac > 0
This will have 2 real positive roots.

ax2 + b|x| + c = 0
This can be written as
ax2 + bx + c = 0
Discriminant = b2 − 4ac > 0.
And,
ax2 − bx + c = 0
(−b)2 − 4ac ⇒ b2 − 4ac is also >0.
So, we will have 4 real roots for ax2 + b|x| + c = 0.

Therefore, correct answer is option (D).

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