Since 𝛼 + 𝛽 are the zeroes of the polynomial: 𝑥2 − 𝑥 − 4
Sum of the roots [α + β] = 1
Product of the roots [αβ] = −4
`1/alpha+1/beta-alphabeta`
`=[alpha+beta]/[alphabeta]-alphabeta`
`=[1/-4]+4=[-1/4]+4=[-1+16]/4=15/4`
Given: $\alpha$ and $\beta$ are zeroes of $x^2-4x+1$.
To do: To find the value of $\frac{1}{\alpha}+\frac{1}{\beta}-\alpha\beta$.
Solution:
Given quadratic polynomial is $x^2-4x+1$.
$\alpha$ and $\beta$ are zeroes of given quadratic polynomial.
$\therefore$ Sum of the zeroes$=\alpha+\beta=-[ \frac{-4}{1}]=4$
Product of the zeroes$=\alpha\beta=\frac{1}{1}=1$
$\therefore \frac{1}{\alpha}+\frac{1}{\beta}-\alpha\beta=\frac{\alpha+\beta}{\alpha\beta}-\alpha\beta$
$=\frac{4}{1}-1$
$=3$
Thus, $\frac{1}{\alpha}+\frac{1}{\beta}-\alpha\beta=3$.
Is Alpha and beta are the zeros of polynomial x2 x 4?
This is Expert Verified Answer
Sol : We have quadratic equation x² - x - 4. Given α and ß are their zeroes. α + ß = 1 / 1 = 1. αß = -4.
Is Alpha and beta are the zeros of polynomial x2 x 1 then find 1 alpha 1 beta?
Given that alpha and beta are the zeros of the polynomial x² - 1. We need to find out the value of 1/alpha + 1/beta. Polynomial: x² - 1 where a is 1, b is 0 and c is -1. Therefore, the value of 1/alpha + 1/beta is 0.
What is the formula of 1 alpha 1 beta?
∴α1−β1=α1−α1−α=αα=1. Was this answer helpful?
Is Alpha and beta are the zeros of polynomial?
alpha and beta are the zeros of a polynomial, such that alpha + beta = 6 and alphabeta = 4 .