Compute the zeroes of the polynomial 4x2 – 4x – 8. Also, establish a relationship between the zeroes and coefficients.
Question
Compute the zeroes of the polynomial 4x² – 4x – 8. Also, establish a relationship between the zeroes and coefficients.
Solution
Sure, let's solve this step by step.
Step 1: Identify the coefficients of the polynomial. In the polynomial 4x^2 – 4x – 8, the coefficients are a = 4, b = -4, and c = -8.
Step 2: Use the quadratic formula to find the roots of the polynomial. The quadratic formula is x = [-b ± sqrt(b^2 - 4ac)] / (2a).
Step 3: Substitute the coefficients into the quadratic formula.
x = [4 ± sqrt((-4)^2 - 44(-8))] / (2*4) x = [4 ± sqrt(16 + 128)] / 8 x = [4 ± sqrt(144)]
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