For what values of $m$ will the equation $x^{2} - 2 x (1 + 3 m) + 7 (3 + 2 m) = 0$ have equal roots?

Open in App

Solution

Given that the equation $x^{2} - 2 x (1 + 3 m) + 7 (3 + 2 m) = 0$ have equal roots.
The given equation have equal roots only if the discriminant is zero
$\Rightarrow b^{2} - 4 a c = (2 + 6 m)^{2} - 4 (21 + 14 m) = 0$
$\Rightarrow 4 + 36 m^{2} + 24 m - 56 m - 84 = 0$
$\Rightarrow 36 m^{2} - 32 m - 80 = 0$
$\Rightarrow 9 m^{2} - 8 m - 20 = 0$
$\Rightarrow m = 2, - \frac{10}{9}$

Suggest Corrections

Similar questions

x^{2} - 2 x (1 + 3 m) + 7 (3 + 2 m) = 0

k

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

x^{2} - 2 (1 + 3 m) x + 7 (3 + 2 m) = 0

m = 2, - \frac{10}{9} .

^{'} 0^{'}

^{'} 1^{'} .

For how many integer values of m does the equation $x^{2} - 10 x + (m + 3) (m - 4) = 0$ have roots of opposite signs?

Join BYJU'S Learning Program