Question

If a and ß are the zeroes of polynomial
4x2 – 5x – 1, find the value of alpha/beta + beta/alpha......... please answer this question quickly......​

Answer 1

Given :

α and ß are the zeroes of polynomial 4x²-5x-1

To find :

The value of $\sf\dfrac{\alpha}{\beta}+\dfrac{\beta}{\alpha}$

Solution :

Let the given Polynomial be $\sf\:f(x)=4x^2-5-1$

We know that ,

$\sf\alpha+\beta =\dfrac{-cofficient\:of\:x}{cofficient\:of\:x^2}$

$\sf\implies\alpha+\beta=\dfrac{-(-5)}{4}=\dfrac{5}{4}...(1)$

$\sf \: and \: \alpha \beta = \dfrac{constant}{cofficient \: of \: x {}^{2} }$

$\sf\implies\alpha\times\beta=\dfrac{-1}{4}..(2)$

We have to find the value of

$\sf\dfrac{\alpha}{\beta}+\dfrac{\beta}{\alpha}$

$\sf=\dfrac{\alpha^2+\beta^2}{\beta\times\alpha}$

$\sf=\dfrac{(\alpha+\beta)^2-2\alpha\times\beta}{\beta\times\alpha}$

Put the values of equation (1) and (2)

$\sf=\dfrac{(\frac{5}{4})^2-2\times\frac{1}{4}}{-\frac{1}{4}}$

$\sf=\dfrac{-33}{4}$

Answer 2

Answer:

Step-by-step explanation:

Given that alpha and beta are zeroes of polynomial 4x² - 5x - 1

have to find the value of alpha/ beta + beta/ alpha

and

Given polynomial is 4x² - 5x - 1

Now,

We know that alpha + beta = -( b ) / a

and alpha * beta = c / a

On comparing we get a=4, b= 5 c= -1

alpha + beta = -( b ) / a

-(5)/4

alpha * beta = c / a

-1/4

TO FIND : alpha/beta + beta/alpha

alpha² + beta²

= –———————

alpha × beta

( alpha + beta )² -2 alpha × beta

—————————————————

alpha × beta

NOW PUT VALUES

(5/4)² -2 × 1/4

————————

-1/4

= -33/4

HOPE IT HELPS