Question

find the zeroes of the polynomial x² -2x - 8 by splitting the middle term method and verify the relationship between zeroes and coefficients
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Answer 1

Answer:

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Answer 2

Step-by-step explanation:

Let the polynomial be p ( x ).

For its zeros ,

p ( x ) = 0

→ x^2 - 2x - 8 = 0

Spilliting the middle term we get

→ x^2 - 4 x + 2x - 8 = 0

Taking common the required values .

→ x ( x - 4 ) + 2 ( x - 4 ) = 0

→ ( x + 2 ) ( x - 4 ) = 0

→ x + 2 = 0. or , x - 4 = 0

→ x = - 2 or , x = 4 .

Hence the zeros of the given polynomial p(x) are - 2 and 4 .

Verification →

1) Sum of zeros = -2 + (4)= 2 = - ( coefficient of x )/( coefficient of x ^2 )

2) Product of zeros = (-2)(4) = -8 = ( constant term ) / (coeiffieciet of x^2)

Hence , the relationship between zeros are coefficient is verified .