Question

if one root of the equation 4x^2-2x-(m-4)=0 be the reciprocalof the other,then the value of m is​

Answer 1

Answer:

IT IS DONE IN THE IMG.. .. .

Answer 2

$\Huge{\underline{\underline{\mathfrak{Answer \colon }}}}$

Let the given polynomial function be p(x)

Given Polynomial,

$\large{ \tt{p(x) = 4x {}^{2} - 2x - (m - 4) }}$

To find

The value of m

Note

• Product of Zeros : constant term/x² coefficient

Given Condition :

The roots of the polynomial are reciprocal to each other

Implies,

Their product is 1

Let one of the zero be $\sf{\alpha}$

• Other zero would be $\frac{1}{\alpha}$

Now,

$\large{ \sf{ \alpha. \frac{1}{ \alpha } = - \frac{ (m - 4)}{4} }} \\ \\ \large{ \leadsto \: \sf{1 = - \frac{(m - 4)}{4} }} \\ \\ \large{ \leadsto \ \sf{m - 4 = - 4}} \\ \\ \huge{ \leadsto \: \boxed{ \boxed{ \tt{ \green{m = 0}}}}}$

Thus,the value of m is 0