The set of values of a, for which (a – 3) x2 + 15x – (6a – a2 – 5) = 0 has roots of opposite sign satisfies

Engineering

Mathematics

Quadratic Equation and Nature of Roots

Question

The set of values of a, for which (a – 3) x² + 15x – (6a – a² – 5) = 0 has roots of opposite sign satisfies

3 < a < 5

1 < a < 3

a > 3

a > 5

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Product of the root less than zero.
$- (\frac{6 a - a^{2} - 5}{a - 3}) < 0$
$\frac{a^{2} - 6 a + 5}{a - 3} < 0$ .
$a \in (- \infty, 1) \cup (3, 5)$ .