Question

If one root of the quadratic equation a x² + bx + c = 0 is the reciprocal of the other, then 
a)b=c
b)a=b
c)ac=1
d)a=c​

Answer 1

Answer:

correct option is D) a=c

Answer 2

$huge\bold{Question:-}$

If one root of the quadratic equation

$a {x}^{2} + bx + c = 0$ is the reciprocal of the other, then 

$a)b = c$

$b)a = b$

$c)ac = 1$

$d)a = c$

$\huge\bold{Solution:-}$

Let one root is $\alpha$

Other root is $\beta$

According to the question

$\alpha = \frac{1}{ \beta }$

So, $\alpha \beta = 1$

We have,

Product of roots $\alpha \beta = \frac{c}{a}$

So,

$\frac{c}{a} = 1$

$c = a$

Final Answer:-

d) $a = c$ is Correct