quadratic polynomial 6x²+x-12 has zeros as a and ß. now form a quadratic polynomial whose zeroes are 3 a and 3ß​

Question

quadratic polynomial 6x²+x-12 has zeros as a and ß. now form a quadratic polynomial whose zeroes are 3 a and 3ß​

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Harper 1 month 2021-08-17T06:46:37+00:00 1 Answer 2 views 0

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    2021-08-17T06:48:22+00:00

    Answer:

    2x^2+x-6=0

    Step-by-step explanation:

    6 {x}^{2}  + x - 12 \\ ( \div ) \: by \: 6  \\  {x }^{2}  + (x \div 6) - 2

    Here,

     \alpha  +  \beta  =  - 1 \div 6 \\  \alpha  \beta  =  - 2

    For the new zeros, ( i.e.)

    for \: 3 \alpha  \: and \: 3 \beta  \\

    For sum of zeros,

    3 \alpha  + 3 \beta    \\  = 3( \alpha +   \beta ) \\  = 3( - 1 \div 6) \\  =  - 1 \div 2

    For product of zeros,

    (3 \alpha )(3 \beta ) \\  = 3( \alpha  \beta ) \\  = 3( - 2) \\  =  - 6

    Then,

     {x}^{2}  - (3 \alpha  + 3 \beta )x + (3 \alpha )(3 \beta ) = 0

    Therefore,

     {x}^{2}  - ( - 1 \div 2)x  +  ( - 6) = 0 \\ ( \times ) \: by \: 2 \\ 2 {x  }^{2}  + x - 6 = 0

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