Question

. If a and Bare the zeroes of the quadratic polynomial f(x) = x ^ 2 - x - 4 , find the Find the value of 1/alpha + 1/beta - alpha*beta​

Answer 1

Answer:

Step-by-step explanation:

given: f(x) = x²- x - 4

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

to find: $\frac{1}{\alpha }+\frac{1}{\beta } - \alpha\beta$

lcm = αβ

$\frac{\beta }{\alpha \beta }+\frac{\alpha }{\alpha \beta } - \frac{\alpha\beta^{2}}{\alpha \beta }$

$\frac{\beta+\alpha }{\alpha \beta }- \frac{\alpha\beta^{2}}{\alpha \beta }$ [equation 1]

sum → α+β → $\frac{-b}{a}$

$\frac{-(-1)}{1}$ = $\frac{1}{1}$ = 1

product → αβ → $\frac{c}{a}$

$\frac{-4}{1}$ = -4

substituting in equation 1...

$\frac{1}{-4} - \frac{(-4)^{2} }{-4}$

$\frac{1}{-4} - \frac{16 }{-4}$

$\frac{1-16}{-4}$

$\frac{-15}{-4}$ = $\frac{15}{4}$

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