29. Obtain all other zeroes of the polynomial x4 + 4xl-2x²-20%-15 if two of it
zeroes are Vs and - V5
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The given polynomial is f(x) = x4 + 4x3 – 2x2 – 20x – 15. Since (x – √5) and (x + √5) are the zeroes of f(x) it follows that each one of (x – √5) and (x + √5) is a factor of f(x). Consequently, (x – √5) (x + √5) = (x2 – 5) is a factor of f(x). On dividing f(x) by (x2 – 5), we get
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