Question

find the zeroes of the quadratic
polynomial 4x^2 - 17x - 21
and verify the relationship between the zeroes and the coefficient


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Answer 1

$\underline{\textsf{Given:}}$

$\textsf{Polynomial is}$

$\mathsf{4x^2-17x-21}$

$\underline{\textsf{To find:}}$

$\textsf{The zeros of the given polynomial}$

$\underline{\textsf{Solution:}}$

$\textsf{Consider,}$

$\mathsf{4x^2-17x-21}$

$\mathsf{=4x^2+4x-21x-21}$

$\mathsf{=4x(x+1)-21(x+1)}$

$\mathsf{=(4x-21)(x+1)}$

$\therefore\textsf{Zeros are}\;\mathsf{-1,\dfrac{21}{4}}$

$\text{Now}$

$\textsf{Sum of the zeros}\;\mathsf{=-1+\dfrac{21}{4}=\dfrac{17}{4}}$

$\textsf{Productof the zeros}\;\mathsf{=-1{\times}\dfrac{21}{4}=\dfrac{-21}{4}}$

$\underline{\textsf{Verification:}}$

$\textsf{Sum of the zeros}\;\mathsf{=\dfac{-b}{a}=\dfrac{-(-17)}{4}=\dfrac{17}{4}}$

$\textsf{Product of the zeros}\;\mathsf{=\dfrac{c}{a}=\dfrac{-21}{4}}$

$\textsf{Hence verified}$

Answer 2

Answer:

S.O.Z = 17/4 P.O.Z= -21/4

Step-by-step explanation:

4X^2-17X-21

4X^2+4X-21X-21

4X(X+1)-21(X+1)

X=-1 and x=21/4

$\alpha \: \: \: \: \: \: \: \beta$

S.O.Z = -1+21/4=17/4

P.O.Z = -1*21/4=-21/4

VERIFICATION

S.O.Z= -b/a = -(-17/4) =17/4

P.O.Z =c/a = -21/4

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