Question

if alfa and beta are the roots x square-3 x - 1 = 0 then form the quadratic equation whose roots are 1/ alfa square and 1/ beta square ​

Answer 1

Given:

$\star \bold{ \alpha \: and \: \beta \: are \: the \: roots \: of \: }$

• x² - 3x - 1

To find :

• The equation whose zeroes are

$\frac{1}{ \alpha } \: and \: \frac{1}{ \beta }$

Solution :

•f (x) = x² - 3x - 1

Now , compare with ax² + bx + c we get :

• a = 1 , b = -3 and c = -1

$\star \bold{ \: sum \: of \: zereos = \alpha + \beta = \frac{ - b}{a} = 3}$

$\star \bold{ product \: of \: zeroes \: = \alpha \beta = \frac{c}{a} = - 1}$

Now , to find the equation whose zeroes are :

$\star \: \frac{1}{ \alpha } and \: \frac{1}{ \beta }$

$\star \bold{ sum \: of \: zeroes} \: = \dfrac{1}{ \alpha } + \dfrac{1}{ \beta } \\ \\ \implies \: \dfrac{ \beta + \alpha }{ \alpha \beta } = \dfrac{3}{ - 1} = - 3 \\ \\ \star \bold{ product \: of \: zeroes} = \dfrac{1}{ \alpha } \dfrac{1}{ \beta } = \dfrac{1}{ \alpha \beta } = \dfrac{1}{ - 1} = - 1$

As we know that :

• F (x ) = x² - ( sum of Zeroes ) x + product of zeroes

=> x² - (-3)x + (-1)

=> x² + 3x -1 .

Answer 2

Step-by-step explanation:

HERE IS U R ANSWER DEAR PLZ FOLLW ME