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JEE Main 20198 AprilEvening Shift

Exam: JEE Main
Year: 2019
Date: 8 April
Shift: Evening Shift
Subject: Mathematics
Chapter: Quadratic Equation

JEE Main 2019 · 8 April · Evening Shift · Mathematics · Quadratic Equation

The number of integral values of m for which the equation, (1 + m ^...

The number of integral values of

m

for which the equation, \left(1 + {m}^{2}\right){x}^{2} - 2\left(1 + 3m\right)x + \left(1 + 8m\right) = 0$ has no real root, is

Options

A $2$
B $3$
CInfinitely many
D $1$

Correct answer

C. Infinitely many

Step-by-step solution

Since the given equation has no real solution.

⇒ D < 0

⇒ 4{\left(1 + 3m\right)}^{2} - 4 \times \left(1 + {m}^{2}\right)\left(1 + 8m\right) < 0

⇒ \left(1 + 9{m}^{2} + 6m\right) - \left(1 + 8m + {m}^{2} + 8{m}^{3}\right) < 0

⇒ - 2m{\left(2m - 1\right)}^{2} < 0

Clearly, for infinite values of

m

given condition is true.

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