Find the sum of the zero of the quadratic polynomiay x²+7x+12​

Question

Find the sum of the zero of the
quadratic
polynomiay x²+7x+12​

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Caroline 1 month 2021-08-13T17:31:43+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-08-13T17:32:53+00:00

    Answer:

    Step-by-step explanation:

    Let f(x)=x^{2} +7x+12

    x^{2} +3x+4x+12                                   {12=3*4}

                                                                   {7=3+4}

    (x^{2} +3x)+(4x+12)\\x(x+3) +4 (x+3)\\(x+3) (x+4)\\either ,\\x+3=0 \\x=-3\\x+4=0\\x=-4

    zeros = -3, -4

    α= -3 ,β= -4

    f(x)=x^{2} +7x+12

       =  1x^{2} +7x+12

    comparing with ax^{2}+bx+c

    so , a=1 , b=7 , c=12

    now finding sum of zeros

    Sum of zero = \frac{-b}{a}

    α +β = \frac{-b}{a}

    -3+(-4)=\frac{-7}{1}

    -7=-7

    product of zeros =  \frac{c}{a}

    α*β=\frac{c}{a}

    (-3)(-4)=\frac{12}{1}

    12=12

    Hope it will help you

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    0
    2021-08-13T17:33:12+00:00

    Answer:

    Given: The polynomial is x² + 7x + 12

    To find : The sum and product of zeroes of the polynomial.

    solution:

    First of all we have to find out the zeroes of the p(x).

    here ,

    ⇒ a = 1

    ⇒b = 7

    ⇒c = 12

    ⇒p( x ) = x² + 7x + 12

    ⇒p ( x ) = 0

    ⇒ x² + 7x + 12 = 0

    ⇒ x² + ( 4 + 3 ) x + 12 =0

    ⇒x² + 4x + 3x + 12 = 0

    ⇒x ( x + 4 ) + 3 ( x + 4 ) = 0

    ⇒( x + 4 ) ( x + 3 ) = 0

    so , Either

    ↦( x + 4 ) = 0

    ↦ x = -4

    or,

    ↦( x + 3 ) = 0

    ↦x = -3

    . • . The zeroes are -4 , -3

    Now ,

    let, the Zeroes be α ,β

    so, α = 4 , β = 3

    \therefore{Sum \:Of \:the \:Zeroes(α+β)}

    = -4 + ( -3)

    = -4 -3

    = -7

    =  \frac{-7 }{1}

    = -7

    =  \frac{-b}{a}

    =  \frac{- Coefficient \:Of \:x}{Coefficient \:Of \:x²}

    \therefore{product \:of \:the \:zeroes(αβ)}

    = -4 × -3

    = 12

    =  \frac{12}{1}

    = 12

    =  \frac{c}{a}

    =  \frac{Constant \:term}{Coefficient \:Of \:x}

    Note:

    For quadratic Equation Or polynomial

    Formulla to find the sum of zeroes is

    = -Coefficient of x / coefficient of x²

    = – b / a

    Formulla to find the product of zeroes

    = constant term / coefficient of x

    = c / a

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