.If α β are the zeroes of the polynomial x2 x 4 then the value of 1 α 1 β αβis equal to
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Since 𝛼 + 𝛽 are the zeroes of the polynomial: 𝑥2 − 𝑥 − 4 Show 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 .
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