Question

If a,b,c are positive and are in A.P, then the roots of ax2+2bx+c=0 are​

Answer 1

Answer:

$x \: \: = \: \: - \frac{c}{a} \: \: \: \: \: or \: \: \: \: x = - 1$

Step-by-step explanation:

$a \: \: b \: \: c \: \: are \: in \: ap \\ therefore \: \: 2b = a + c \\ \\ \\ a {x}^{2} +( 2b)x + c = 0 \\ \\ a {x}^{2} + (a + c)x + c = 0\:\:\:\:\: \:( put\:\: \:2b \:=\:a+c)\\ \\ a {x}^{2} + ax + cx + c = 0 \\ \\ ax(x +1 ) + c(x + 1) = 0 \\ \\ (ax + c)(x + 1) = 0 \\ \\ x = - \frac{c}{a \: \: \:} \: \: \: \: or \: \: \: x = - 1$