Question

if two roots of 2x^2+bx+c=0 are reciprocal of each other then find the value of c

Answer 1

Let the roots be (x)&(1/x) i.e., @&ß (roots)
Here, a=2, b=b, c=c

@ß = c/a. (product of roots)
x(1/x) = c/2
1 = c/2
C = 2

Answer 2

Answer:

c=2

Step-by-step explanation:

We know that standard Quadratic equation

$a {x}^{2} + bx + c = 0$

it has two roots,let the roots are

$\alpha\:and\: \beta$

We know that relation between coefficient and zeros are

$\alpha + \beta = \frac{ - b}{a} \\ \\ \alpha \beta = \frac{c}{a}$

According to the question roots are reciprocal of each other, so if one roots is

$\alpha$

and other root will be

$\frac{1}{ \alpha }$

Multiply both roots

$\alpha ( \frac{1}{ \alpha } ) = \frac{c}{2} \\ \\ 1 = \frac{c}{2} \\ \\ c = 2$

Hope it helps you.