Math, asked by ashagupta92, 1 year ago

if the zeroes of the polynomial x2+px+q are double in value to the zeroes of 2x2 - 5x-3,find the value of p and q ​

Answers

Answered by amitnrw
4

Given : zeroes of the polynomial x²+px+q are double in value to the zeroes of 2x² - 5x-3

To Find :   value of p and q

Solution:

zeroes of 2x² - 5x-3  

α , β

Sum of Zeroes = α +  β  =  - (-5/2) =  5/2

Product   of Zeroes = αβ  =  -3/2

zeroes of the polynomial x²+px+q are double in value to the zeroes of 2x² - 5x-3

Hence 2α  , 2β

Sum of Zeroes = 2α +  2β  = 2 ( α +  β  )  = 2 (5/2) = 5  =   - p/1

=> p = - 5

Product   of Zeroes = 2α *  2β = 4αβ  =  4  * ( -3/2)    = -6  = q

=> q = -6

Value of p  = - 5

and value of q = -6

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Answered by MaheswariS
3

\textbf{Given:}

\mathsf{Zeroes\;of\;x^2+px+q\;are\;double\;in\;value\;to\;the\;zerroes\;of\;2x^2-5x-3}

\textbf{To find:}

\textsf{The value of p and q}

\textbf{Solution:}

\textsf{First we find out zeroes of}\;\mathsf{2x^2-5x-3}

\mathsf{2x^2-5x-3}

\mathsf{=2x^2-6x+x-3}

\mathsf{=2x(x-3)+1(x-3)}

\mathsf{=(2x+1)(x-3)}

\mathsf{2x^2-5x-3=0\;\implies\;x=\dfrac{-1}{2},3}

\therefore\mathsf{Zeroes\;of\;2x^2-5x-3\;are\;\dfrac{-1}{2}\;and\;3}

\implies\mathsf{Zeroes\;of\;x^2+px+q\;are\;2\left(\dfrac{-1}{2}\right)\;and\;2(3)}

\implies\mathsf{Zeroes\;of\;x^2+px+q\;are\;-1\;and\;6}

\mathsf{Now,}

\mathsf{Sum\;of\;zeroes=5}

\mathsf{\dfrac{-p}{1}=5}

\implies\boxed{\mathsf{p=-5}}

\mathsf{Product\;of\;zeroes=5}

\mathsf{\dfrac{q}{1}=-6}

\implies\boxed{\mathsf{q=-6}}

\textbf{Find more:}

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