Question

If one root of the equation 4x^2 – 2x + (β - 4 ) = 0 be the reciprocal of the other, then find β.

Answer 1

By using above method, it can be solved by this way.

Answer 2

The value of "$\beta$ is equal to 8".

Step-by-step explanation:

Let first root = α and

Other root = $\dfrac{1}{\alpha}$

To find, the value of β = ?

The given quadratic equation:

$4x^2-2x+(\beta -4)=0$

Here, a = 4, b = - 2 and c = $\beta -4$

We know that,

The product of roots = $\dfrac{c}{a}$

∴$\alpha} \times \dfrac{1}{\alpha}=\dfrac{\beta -4}{4}$

⇒ $1=\dfrac{\beta -4}{4}$

⇒$\beta -4=4$

⇒$\beta =4+4=8$

Hence, the value of "$\beta$ is equal to 8".