find a quadratic polynomial whose zeros -4 and 3 and verify the relation ship between the zeros and the coefficients​

Question

find a quadratic polynomial whose zeros -4 and 3 and verify the relation ship between the zeros and the coefficients​

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Nevaeh 11 months 2021-06-22T06:38:29+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-06-22T06:39:52+00:00

    Step-by-step explanation:

    Given :

    Zeros -4 and 3

    To find :

    Find a quadratic polynomial whose zeros -4 and 3 and verify the relation ship between the zeros and the coefficients ?

    Solution:

    Given zeroes are -4 and 3

    Let α = -4

    and Let β = 3

    We know that

    The Quadratic Polynomial whose zeroes α and β

    is K[x^2-(α +β)x +α β]

    On Substituting these values in the above formula

    => K[x^2-(-4+3)x+(-3)(4)]

    => K[x^2-(-1)x+(-12)]

    => K[x^2+x-12]

    If K = 1 then the quardratic polynomial is x^2+x-12.

    Relationship between the zeroes and the coefficients of x^2+x-12:

    Quadratic polynomial = x^2+x-12

    On Comparing this with the standard quadratic Polynomial ax^2+bx+c

    a = 1

    b = 1

    c=-12

    And

    α = -4

    β = 3

    i) Sum of the zeroes

    => α +β

    => -3+4

    => – 1

    => -1/1

    => -(coefficient of x)/Coefficient of x^2

    => -b/a

    Verified the relation.

    And

    ii) Product of the zeroes

    =>α β

    => (-4)(3)

    => -12

    => -12/1

    => Constant term/ Coefficient of x^2

    => c/a

    Verified the relationship between the zeroes and the coefficients.

    Answer:

    The quardratic polynomial is x^2+x-12

    Used formulae:

    • the standard quadratic Polynomial ax^2+bx+c
    • Sum of the zeroes = α +β= -b/a
    • Product of the zeroes = α β = c/a
    0
    2021-06-22T06:40:24+00:00

    Answer:

    x2-sx +p

    x2+4x+3 is the quadratic polynomial

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