Q1. Find the zeroes of the quadratic polynomial f(x) = 4y2 – 4y + 1 and verify the relationship between zeroes and the coefficients.

Question

Q1. Find the zeroes of the quadratic polynomial f(x) = 4y2 – 4y + 1 and verify the relationship
between zeroes and the coefficients.
D 255​

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Jade 4 weeks 2021-08-16T18:48:08+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-08-16T18:49:08+00:00

    S O L U T I O N :

    We have quadratic polynomial p(x) = 4y² – 4y + 1 & zero of the polynomial p(x) = 0

    \underline{\underline{\tt{Using\:\:by\:\:factorization\:\:method\::}}}

    \mapsto\sf{4y^{2} -4y + 1=0}

    \mapsto\sf{4y^{2} -2y-2y +1=0}

    \mapsto\sf{2y(2y -1) -1(2y-1)=0}

    \mapsto\sf{(2y -1) (2y-1)=0}

    \mapsto\sf{2y-1=0\:\:\:Or\:\:\:2y-1=0}

    \mapsto\sf{2y=1\:\:\:Or\:\:\:2y=1}

    \mapsto\bf{y=1/2\:\:\:Or\:\:\:y=1/2}

    ∴ α = 1/2 & β = 1/2 are the zeroes of the given polynomial .

    As we know that given polynomial compared with ax² + bx + c;

    • a = 4
    • b = -4
    • c = 1

    Now;

    \underline{\mathcal{SUM\:OF\:THE\:ZEROES\::}}

    \mapsto\tt{\alpha + \beta =\dfrac{-b}{a} =\bigg\lgroup \dfrac{Coefficient\:of\:x}{Coefficient\:of\:x^{2}} \bigg\rgroup }

    \mapsto\tt{\dfrac{1}{2}  + \dfrac{1}{2}  =\dfrac{-(-4)}{4}}

    \mapsto\tt{\dfrac{1+ 1}{2}   =\dfrac{-(-4)}{4}}

    \mapsto\tt{\cancel{\dfrac{2}{2}}   =\cancel{\dfrac{4}{4}}}

    \mapsto\bf{1  =1}

    \underline{\mathcal{PRODUCT\:OF\:THE\:ZEROES\::}}

    \mapsto\tt{\alpha \times \beta =\dfrac{c}{a} =\bigg\lgroup \dfrac{Constant\:term}{Coefficient\:of\:x^{2}} \bigg\rgroup }

    \mapsto\tt{\dfrac{1}{2}  \times  \dfrac{1}{2}  =\dfrac{1}{4}}

    \mapsto\bf{\dfrac{1}{4}   =\dfrac{1}{4}}

    Thus;

    The relationship between zeroes & coefficient are verified .

    0
    2021-08-16T18:49:44+00:00

    Answer:

    If α and β are the zeros of ax2 + bx + c, a ≠ 0 then verify the relation between the zeros and its coefficients. Sol. Since a and b are the zeros of polynomial ax2 + bx + c. Therefore, (x – α), (x – β) are the factors of the polynomial ax2 + bx + c.

    Step-by-step explanation:

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