Find the zeroes of the quadratic polynimial 3x²-x-4 and verify the relationship between the zeroes and the coefficien

Question

Find the zeroes of the quadratic polynimial 3x²-x-4 and verify the relationship between the zeroes and the coefficien

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Aubrey 7 months 2021-10-13T17:57:56+00:00 2 Answers 0 views 0

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    0
    2021-10-13T17:58:56+00:00

    Answer :

    Note:

    ★ The possible values of the variable for which the polynomial becomes zero are called its zeros .

    ★ A quadratic polynomial can have atmost two zeros .

    ★ The general form of a quadratic polynomial is given as ; ax² + bx + c .

    ★ If α and ß are the zeros of the quadratic polynomial ax² + bx + c , then ;

    • Sum of zeros , (α + ß) = -b/a

    • Product of zeros , (αß) = c/a

    ★ If α and ß are the zeros of a quadratic polynomial , then that quadratic polynomial is given as : k•[ x² – (α + ß)x + αß ] , k ≠ 0.

    ★ The discriminant , D of the quadratic polynomial ax² + bx + c is given by ;

    D = b² – 4ac

    ★ If D = 0 , then the zeros are real and equal .

    ★ If D > 0 , then the zeros are real and distinct .

    ★ If D < 0 , then the zeros are unreal (imaginary) .

    Solution :

    Here ,

    The given quadratic polynomial is ;

    3x² – x – 4 .

    Clearly ,

    a = 3

    b = -1

    c = -4

    For finding zeros of the given quadratic polynomial , equate it to zero .

    Thus ,

    => 3x² – x – 4 = 0

    => 3x² – 4x + 3x – 4 = 0

    => x(3x – 4) + (3x – 4) = 0

    => (3x – 4)(x + 1) = 0

    => x = 4/3 , -1

    Now ,

    • Sum of zeros = 4/3 + (-1)

    = 4/3 – 1

    = (4 – 3)/3

    = 1/3

    • -b/a = -(-1)/3 = 1/3

    Clearly , Sum of zeros = -b/a

    Also ,

    • Product of zeros = (4/3)×(-1) = -4/3

    • c/a = -4/3

    Clearly , Product of zeros = c/a

    Hence verified .

    0
    2021-10-13T17:59:55+00:00

    Answer:

    Step-by-step explanation:

    3x^2-x-4=0

    3x^2+3x-4x-4=0

    3x(x+1)-4(x+1)=0

    (3x-4)(x+1)=0

    3x-4=0

    x=4/3

    x+1=0

    x=-1

    The sum of the zeroes of given polynomial=-b/a

    -1+4/3=-(-1)/3

    (-3+4)/3=1/3

    1/3=1/3

    Product of the zeroes of given polynomial=c/a

    -1×4/3=-4/3

    -4/3=-4/3

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