Question

If 3 and -3 are two zeroes of the polynomial (x⁴ + x³ - 34x² - 4x + 120), find all the zeroes of the given polynomial

Answer 1

Answer: 2 and -2

Step-by-step explanation:

Since the degree of the polynomial if 4, there will be 4 zeroes for this polynomial.

p(2) = 2⁴ + 2³ - {34*(2²)} - (4*2) + 120

      = 16 + 8 - 136 - 8 + 120

      = 0

p(-2) = -2⁴ + -2³ - {34*(-2²)} - (4*-2) + 120

      = 16 - 8 - 136 + 8 + 120

      = 0

Therefore, the zeroes of the polynomial (x⁴ + x³ - 34x² - 4x + 120), are 2, -2, 3 and -3.

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