Number of values of $a$ for which given equation have equal roots $x^{2} - 2 x - (4 a^{2} - 16 a + 15) = 0$

Open in App

Solution

$x^{2} - 2 x - (4 a^{2} - 16 a + 15) = 0$
For roots to be equal,
$b^{2} - 4 a c = 0$
$4 + 4 (1) (4 a^{2} - 16 a + 15) = 0$
$⟹ 4 a^{2} - 16 a + 15 = 0$
$⟹ 4 a^{2} - 10 a - 6 a + 15 = 0$
$⟹ 2 a (2 a - 5) - 3 (2 a - 5) = 0$
$⟹ (2 a - 3) (2 a - 5) = 0$
$⟹ a = \frac{3}{2}, a = \frac{5}{2}$

Suggest Corrections

Similar questions

x^{2} - 15 - m (2 x - 8) = 0

a

x^{2} + 3 x - (a^{2} + a - 2) = 0

x^{2} + 2 x + 4 p = 0

x^{2} + p x (1 + 3 k) + 7 (3 + 2 k) = 0

m

x^{2} - m (2 x - 8) - 15 = 0

a

x^{2} + a x + 16 = 0

Join BYJU'S Learning Program