JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
The number of integral values of \(m\) for which the equation \((1 + m^2) x^2 - 2(1 + 3m) x + (1 + 8m) = 0\) has no real root is
- A infinitely many
- B \(2\)
- C \(3\)
- D \(1\)
Answer & Solution
Correct Answer
(A) infinitely many
Step-by-step Solution
Detailed explanation
\(D=4(1+3 m)^{2}-4\left(1+m^{2}\right)(1+8 m)\) \(=4\left(1+9 m^{2}+6 m-1-8 m-m^{2}-8 m^{3}\right)\) \(=-8 m\left(4 m^{2}-4 m+1\right)\) \(=-8 m(2 m-1)^{2}<0\) \(\therefore \) Infinitely many values of \(\mathrm{m}\)
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