Find the values of $m$ for which the quadratic equation $x^{2} - m (2 x - 8) - 15 = 0$ has (i) equal roots; (ii) both roots positive

Open in App

Solution

(i) For equal roots, $b^{2} - 4 a c = 0$ ,
$4 m^{2} - 4 (8 m - 15) = 0$
$4 m^{2} - 8 m + 15 = 0$
$m^{2} - 8 m + 15 = 0$
$(m - 3) (m - 5) = 0$
$m = 3, m = 5$
(ii) For roots positive
$b^{2} - 4 a c > 0$
$m \in (3, \infty), m \in (5, \infty)$

Suggest Corrections

Similar questions

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

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

(ii) Write all the values of k for which the quadratic equation x² + kx + 16 = 0 has equal roots. Find the roots of the equation so obtained.

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

m =

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

x^{2} + k (2 x + k - 1) + 2 = 0

m

x^{2} + 2 (m - 1) x + (m + 5) = 0

Join BYJU'S Learning Program