Find the zeroes of the quadratic polynomial and verify the relation between the zeroes and the coefficients 9x^2-3x-2

Question

Find the zeroes of the quadratic polynomial and verify the relation between the zeroes and the coefficients 9x^2-3x-2

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Margaret 8 months 2021-09-23T12:41:05+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-09-23T12:42:27+00:00

    Step-by-step explanation:

    Comparing the equation by ax^2+bx+c

    We get,

    a=9 b=-3 c=-2

    9x^2-3x-2

    9x^2-6x+3x-2(on factorising)

    3x(3x-2) +1(3x-2)

    3x+1=o

    so x=-1/3(alfa)

    3x-2=0

    so, x=2/3(beta)

    Sum of zeroes=-b/a

    alfa + beta=-b/a

    -1/3+(2/3)=3/9

    1/3=1/3

    Product of zeroes=c/a

    alfa*beta=c/a

    -1/3*(2/3)=-2/9

    -2/9=-2/9

    Hence, proved

    0
    2021-09-23T12:42:29+00:00

    \underline\mathfrak{Given:-}

    • P (x) => 9x² – 3x – 2

    \underline\mathfrak{To \: \: Find:-}

    • Find the zeroes are coefficients ……?

    \underline\mathfrak{Solutions:-}

    • \: \: \: \: \: P \: {(x)} \: \: = \: \: {9x}^{2} \: - \: {3x} \: - \: {2}

    \: \: \: \: \: \leadsto \: \: {9x}^{2} \: - \: {3x} \: - \: {2}

    \: \: \: \: \: \leadsto \: \: {9x}^{2} \: - \: {6x} \: + \: {3x} \: - \: {2}

    \: \: \: \: \: \leadsto \: \: {3x} \: {({3x} \: - \: {2})} \: + \: {1} \: {({3x} \: - \: {2})}

    \: \: \: \: \: \leadsto \: \: {({3x} \: + \: {1})} \: \: \: {({3x} \: - \: {2})}

    \: \: \: \: \: \: \leadsto \: \: {x} \: \: = \: \: \frac{-1}{3} \: \: \: and \: \: \: {x} \: \: = \: \: \frac{2}{3}

    \: \: \: \: \: \: \: \: \: {\alpha} \: \: = \: \: \frac{-3}{2} \: \: \: and \: \: \: {\beta} \: \: = \: \: \frac{2}{3}

    \underline\mathfrak{Verification:-}

    • \: \: \: \: \: P \: {(x)} \: \: = \: \: {9x}^{2} \: - \: {3x} \: - \: {2}
    • a = 9
    • b = -3
    • c = -2

    \: \: \: \: \: \therefore {Sum \: \: of \: \: zeroes} \: \: = \: \: \frac{ \: - \: coefficient \: \: of \: \: x}{coefficient \: \: of \: \: {x}^{2}}

    \: \: \: \: \: \leadsto \: \: {\alpha} \: + \: {\beta}  \: \: = \: \: \frac{-b}{a}

    \: \: \: \: \: \leadsto \: \: \frac{-1}{3} \: + \: \frac{2}{3}  \: \: = \: \: \frac{- \: {(-3)}}{9}

    \: \: \: \: \: \leadsto \: \: \frac{{-3} \: + \: {2}}{3}  \: \: = \: \: \frac{3}{9}

    \: \: \: \: \: \leadsto \: \: \frac{1}{3}  \: \: = \: \: \cancel{\frac{3}{9}}

    \: \: \: \: \: \leadsto \: \: \frac{1}{3}  \: \: = \: \: \frac{1}{3}

    \: \: \: \: \: \therefore {Product \: \: of \: \: zeroes} \: \: = \: \: \frac{constant \: \: term}{coefficient \: \: of \: \: {x}^{2}}

    \: \: \: \: \: \leadsto \: \: {\alpha} \: {\beta}  \: \: = \: \: \frac{c}{a}

    \: \: \: \: \: \leadsto \: \: \frac{-1}{3} \: \times \: \frac{2}{3}  \: \: = \: \: \frac{-2}{3}

    \: \: \: \: \: \leadsto \: \: \frac{-2}{9} \: \: = \: \: \frac{-2}{9}

    Verified.

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