Question

If apha and beta are zeroes of x2 -4x+1 then 1/alpha+1/beta -alpha beta is

Answer 1

Question :-

$\sf{if \: \alpha \: and \: \beta \: are \: the \: zeros \: of \: } \\ \sf{ {x}^{2} - 4x + 1 = 0 \: then \: find \:} \\ \frac{1}{ \alpha} + \frac{1}{ \beta} - \alpha \beta \:$

Answer :-

$\to \: \boxed{ \frac{1}{ \alpha} + \frac{1}{ \beta} - \alpha \beta \: = 3} \:$

Explanation :-

We have a quadratic polynomial

→ x² - 4x + 1 = 0

$\star \sf{ \: \: sum \: of \: zeros = \frac{ - coefficient\:of\:x}{coefficient\:of\:{x}^{2}} } \\ \: \: \: \: \boxed{\alpha + \beta = 4} \\ \\ \star \sf{ \: product \: of \: zeros = \frac{Constant}{coefficient\:of\:{x}^{2}} } \\ \: \: \boxed{ \alpha \beta = 1}$

now ,we have

$\implies \: \: \frac{1}{ \alpha} + \frac{1}{ \beta} - \alpha \beta \: \: \\ \\ \implies \: \: \frac{ \alpha + \beta}{ \alpha \beta} - \alpha \beta \\ \\ \implies \: \frac{4}{1} - 1 \\ \\ \implies \: 3 \\ \therefore \\ \to \: \boxed{ \frac{1}{ \alpha} + \frac{1}{ \beta} - \alpha \beta \: = 3}$

Answer 2

$\tt{\huge{\orange {Hello!!! }}} S.D$

QUESTION :

If apha and beta are zeroes of x2 -4x+1 then 1/alpha+1/beta -alpha beta is......

SOLUTION :

$f(x) = X^2 - 4 X + 1 \\ \\ </p><p></p><p>{ \alpha } + { \beta } = \dfrac{-b}{a} = 4 \\ \\ </p><p></p><p>{\apha} {\beta} = \dfrac{c}{a} = 1$

$\dfrac{1}{ \alpha} + \dfrac{1}{ \beta} = \dfrac{ { \alpha } + { \beta } }{ {\apha} {\beta} } = 4</p><p> [/ tex]</p><p></p><p>Hence : </p><p></p><p>[tex] \dfrac{1}{ \alpha} + \dfrac{1}{ \beta} - {\apha} {\beta} = 4 - 1 = 3$

Hence the answer is 3.