Question

f(x) = x^2- x- 4. Find 1/ alpha +1/ beta - alpha beta​

Answer 1

Answer:

see the attachment for answer

Explanation:

plzz mark as brainlist..

Answer 2

ANSWER :–

15/4

EXPLANATION :–

GIVEN :–

• A function – f(x) = x² - x - 4

TO FIND :–

$\\ { \bold { \frac{1}{ \alpha } + \frac{1}{ \beta } - \alpha \beta }}$

SOLUTION :–

$\\ { \bold { = \frac{ \alpha + \beta }{ \alpha \beta } - \: \alpha \beta }}$

▪︎ If a quadratic equation f(x) = ax² + bx + c have two roots $\alpha$ and $\beta$ then –

• Sum of roots = $\alpha + \beta$ = -b/a

• Product of roots = $\alpha \beta$

▪︎ Now According to the question –

${ \bold \: {= \frac{ \frac{ - b}{a} }{ \frac{c}{a} } - \frac{c}{a} }}$

${ \bold \: {= \frac{ - b}{c} - \frac{c}{a} }}$

• Now put the values –

=> a = 1 , b = -1 and c = -4

${ \bold \: {= \frac{- ( - 1)}{ - 4} - \frac{ (- 4)}{1} }}$

${ \bold \: {= \frac{ - 1}{ 4} + 4 }}$

${ \bold \: {= \frac{ 15}{ 4} }}$