If alpha and beta are the roots of the equation x minus A into x minus b + c equal to zero then the roots of the equation x minus Alpha into

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If alpha and beta are the roots of the equation x minus A into x minus b + c equal to zero then the roots of the equation x minus Alpha into x minus beta equal to c are

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Maya 1 month 2021-08-18T16:15:35+00:00 1 Answer 0 views 0

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    2021-08-18T16:17:06+00:00

    \textbf{Given:}

    \text{$\alpha$ and $\beta$ are roots of $(x-a)(x-b)+c=0$}

    \textbf{To find:}

    \text{The roots of the equation $(x-\alpha)(x-\beta)=c$}

    \textbf{Solution:}

    \text{Consider,}

    (x-a)(x-b)+c=0

    x^2-(a+b)x+(ab+c)=0

    \text{Then,}

    \alpha+\beta=\dfrac{a+b}{1}

    \implies\bf\alpha+\beta=a+b

    \alpha\beta=\dfrac{ab+c}{1}

    \implies\bf\alpha\beta=ab+c

    \text{Now,}

    (x-\alpha)(x-\beta)=c

    x^2-(\alpha+\beta)x+\alpha\beta=c

    x^2-(a+b)x+ab+c=c

    x^2-(a+b)x+ab=0

    x(x-a)-b(x-a)=0

    (x-a)(x-b)=0

    \implies\bf\,x=a,\;b

    \textbf{Answer:}

    \textbf{The roots of $(x-\alpha)(x-\beta)=c$ are $\bf\,a$ and $\bf\,b$}

    \textbf{Find more:}

    1)If alpha and beta are zeroes of quadratic polynomial x2 -(k+6x)+2(2k-1) 

    find k if alpha +beta=1/2alpha beta 

    2)If alpha and beta are zeroes of x2-6x+a, find the value of a if 3alpha+2beta=20

    https://brainly.in/question/16419985

    If α and β are the zeroes of the polynomial

    xsquare+ x – 1, the evaluate α + β + αβ

    https://brainly.in/question/17511372

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