Question

QUESTION :


Compute the zeroes of the polynomial 4x^2 – 4x – 8. Also, establish a relationship between the zeroes and coefficients.


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Answer 1

Answer:

Zeroes of the polynomial are x=1 or x=x=-1/2

Relation between zeroes and coefficients are

-b/a and c/a

Answer 2

✪Solution:-

$4x^2– 4x – 8 = 0 \\ 4(x^2– x – 2) = 0 \\ x^2– x – 2 =0 \\ x^2– 2x + x – 2 = 0 \\ x(x – 2) + 1(x – 2) = 0 \\ (x – 2)(x + 1) = 0 \\ x = 2, x = -1$

Now,

Sum of zeros,

$= 2 - 1 \\ \\ = 1 \\ \\ = \frac{( - 4)}{4} = \frac{ Coefficient\: of \: x}{ Coefficient\: of \: {x}^{2} }$

Product of Zeros,

$= 2 \times ( - 1) \\ \ \\ \ = - 2 \ \\ \ \\ = \frac{ - 8}{4} = \frac{Constant \: term}{Coefficient \: of \: x}$