Question

if alpha and beta of a polynomial x^2-7x+k are such that alpha-beta =1 then find the value of K

Answer 1

$\underline{\textbf{Given:}}$

$\mathsf{\alpha\;and\;\beta\;are\;zeroes\;of\;x^2-7x+k\;and\;\alpha-\beta=1}$

$\underline{\textbf{To find:}}$

$\textsf{The value of k}$

$\underline{\textbf{Solution:}}$

$\mathsf{Consider,\;x^2-7x+k}$

$\boxed{\mathsf{Sum\;of\;zeroes=\dfrac{-b}{a}}}$

$\mathsf{\alpha+\beta=\dfrac{7}{1}}$

$\mathsf{\alpha+\beta=7}$

$\boxed{\mathsf{Product\;of\;zeroes=\dfrac{c}{a}}}$

$\mathsf{\alpha\,\beta=\dfrac{k}{1}}$

$\mathsf{\alpha\,\beta=k}$

$\mathsf{Now,}$

$\mathsf{(\alpha-\beta)^2=(\alpha+\beta)^2-4\alpha\,\beta}$

$\mathsf{(1)^2=(7)^2-4\,k}$

$\mathsf{1=49-4\,k}$

$\mathsf{4\,k=49-1}$

$\mathsf{4\,k=48}$

$\mathsf{k=\dfrac{48}{4}}$

$\implies\boxed{\boxed{\mathsf{k=12}}}$

$\underline{\textbf{Find more:}}$

if alpha and beta are the zeros of the polynomial 3x^2 - 4x - 7 then form a quadratic equation whose zeroes are 1/alpha and 1/beta

https://brainly.in/question/4436832

Answer 2

Step-by-step explanation:

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