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CBSE Class 10 Answered

p(X)=x2-(k+6)(X+2)(2k-1) then find the value of k is alpha+beta =1/2 alpha beta
Asked by rekhapreetham | 15 Jun, 2023, 08:23: PM
answered-by-expert Expert Answer
This can be solved as follows:

p(x) = x2-(k+6)(X+2)(2k-1)

= x2 – (k+6)(2k-1)(x+2)

= x2 – (2k2 + 11k – 6)(x + 2)

= x2 – (2k2 + 11k – 6)x – (4k2 + 22k – 12)

As space straight alpha space and space straight beta space are space the space zeroes space of space this space polynomial rightwards double arrow straight alpha plus straight beta equals left parenthesis 2 straight k squared space plus space 11 straight k space – space 6 right parenthesis space space and space space αβ equals – left parenthesis 4 straight k squared space plus space 22 straight k space – space 12 right parenthesis space Since comma space straight alpha plus straight beta equals 1 half αβ space space space... space left parenthesis Given right parenthesis rightwards double arrow space left parenthesis 2 straight k squared plus 11 straight k – 6 right parenthesis equals 6 minus 2 straight k squared minus 11 straight k rightwards double arrow space 2 straight k squared plus 11 straight k space – space 6 space equals space 0 rightwards double arrow space 2 straight k squared plus 12 straight k space – space straight k space – space 6 space equals space 0 space space rightwards double arrow space 2 straight k left parenthesis straight k space plus space 6 right parenthesis space – space left parenthesis straight k space plus space 6 right parenthesis space equals space 0 rightwards double arrow space left parenthesis straight k plus 6 right parenthesis left parenthesis 2 straight k minus 1 right parenthesis equals 0 rightwards double arrow straight k equals negative 6 space or space straight k equals 1 half

Answered by Renu Varma | 16 Jun, 2023, 09:34: AM

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