Question

Compute the zeroes of the polynomial 4x2 – 4x – 8. Also, establish a relationship between the zeroes and coefficients.​

Answer 1

Answer:

$4 {x}^{2} - 4x - 8 = 0 \\ 4( {x}^{2} - x - 2) = 0 \\ {x }^{2} - 2x + x - 2 = 0 \\ x(x - 2) + 1(x - 2) = 0 \\ (x - 2)(x + 1) = 0 \\ x = 2 \: and \: - 1$

Sum of roots = - coefficient of x/coefficient of x^2

2+(-1)= - (-4)/4=1

Product of roots = constant /coefficient of x^2

2(-1)=-8/4= - 2

Answer 2

Answer:

4 {x}^{2}  - 4x - 8 = 0 \\ 4( {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 \: and \:  - 1 \\  

Sum of roots = - coefficient of x/coefficient of x^2

2+(-1)= - (-4)/4=1

Product of roots = constant /coefficient of x^2

2(-1)=-8/4= - 2

Step-by-step explanation:

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