if X and B are the zeros of the qaudratic polynomial f(x)=x2-3x+2,then find x2+b2​

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if X and B are the zeros of the qaudratic polynomial f(x)=x2-3x+2,then find x2+b2​

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Vivian 1 month 2021-08-19T08:25:23+00:00 1 Answer 0 views 0

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    2021-08-19T08:27:15+00:00

    Answer:Given:


    If m and n are the zeroes of


    quadratic polynomial f(x)=x²-3x-2


    To find :


    Quadratic polynomial whose


    zeroes are 1/(2m+n) and 1/(2n+m) .


    Explanation:


    Compare f(x)= x²-3x-2 with


    ax²+bx+c, we get


    a = 1 , b = -3 , c = -2


    i) m+n = -b/a = -(-3)/1 = 3–(1)


    ii) mn = c/a = -2/1 = -2–(2)


    iii) m²+n² = (m+n)²-2mn


    = 3² – 2×(-2)


    = 9 + 4


    = 13 —-(3)


    Now ,


    1/(2m+n) , 1/(2n+m) are zeroes


    of a polynomial.


    1) Sum of the zeroes


    = 1/(2m+n) + 1/(2n+m)


    = [2n+m+2m+n]/[(2m+n)(2n+m)]


    = [3m+3n]/[4mn+2m²+2n²+mn]


    = [3(m+n)]/[2(m²+n²)+5mn]


    = [3×3]/[2×13 + 5(-2)]


    = 9/(26-10)


    = 9/16 —-(4)


    2) Product of the zeroes


    = [1/(2m+n) × 1/(2n+m)]


    = 1/( 4mn+2m²+2n²+mn)


    = 1/[2(m²+n²) + 5mn ]


    = 1/[ 2×13 + 5(-2)]


    = 1/(26-10)


    = 1/16 —(5)


    ______________________


    Form of a quadratic polynomial


    is


    k[x²-(sum of the zeroes)x+product of the zeroes]


    ______________________


    Here ,


    Required polynomial is


    k[ x²-(9/16)x+1/16]


    For all real values of k it is true.


    let k = 16,


    16[x²-(9/16)x+1/16]


    = 16x²-9x+1


    Therefore,


    Polynomial whose zeroes are


    1/(2m+n) and 1/(2n+m) is


    16x²-9x+1

    hope it helps u

    plz mark as brainlaist answer

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