If roots of the equation $a x^{2} + 2 (a + b) x + (a + 2 b + c) = 0$ are imaginary, then find nature of roots of the equation $a x^{2} + 2 b x + c = 0$ .

Open in App

Solution

$a x^{2} + 2 \times (a + b) + . . . (a + 2 b + c) = 0.... (i) a x^{2} + 2 b x + c = 0.... (i i) r o o t s o f e q u a t i o n (i) a r e a m a g i n a r y s o, B^{2} - 4 A C < 0 o n D < 0 {[2 (a + b)]}^{2} - 4 \times a \times (a + 2 b + c) < 0 4 a^{2} + 4 b^{2} + B a b - 4 a^{2} - 8 a b - 4 a c < 0 4 (b^{2} - a c) < 0 b^{2} < a c \to (i i i) f o r e q u a t i o n \to (i i) D = B^{2} 4 a c = 4 b^{2} - 4 a c = 4 (b^{2} - a c) [∵ b^{2} - 9 c < 0] s o, D < 0 o r r o o t s o f e q u a t i o n (i i) w i l l b e i m a g i n a r y .$

Suggest Corrections

Similar questions

a x^{2} + 2 b x + c = 0

a x^{2} + 2 (a + b) x + (a + 2 b + c) = 0

a, b, c \in R^{+}

2 b = a + c

a x^{2} + 2 b x + c = 0

a^{2} + b^{2} + c^{2} < 0

a x^{2} + b x + c = 0

a x^{2} + b x + c = 0

a, b, c

0 < a < b < c

α, β

a x^{2} + b x + c = 0

a x^{2} + b x + c = 0

Join BYJU'S Learning Program