Answer :

Final answer:

The zeroes of the equation 2x^4 + 70x^2 - 72 = 0 are x = 1 and x = -36.

Explanation:

To find the zeroes of the equation 2x4 + 70x2 - 72 = 0, we can use the quadratic formula. The equation is in the form ax2 + bx + c = 0, where a = 2, b = 70, and c = -72. Plugging these values into the quadratic formula, we get x = (-b ± √(b^2 - 4ac)) / (2a). After substituting the values, we can simplify the expression and find the values of x.

  1. Let a = 2, b = 70, and c = -72 in the quadratic formula: x = (-70 ± √(70^2 - 4(2)(-72))) / (2(2)).
  2. Calculate the discriminant: (70^2 - 4(2)(-72)) = 4900 + 576 = 5476.
  3. Take the square root of the discriminant: √5476 ≈ 74.
  4. Plug the values back into the quadratic formula: x = (-70 ± 74) / 4.
  5. Simplify the expression: x = 1 or x = -36.

Therefore, the zeroes of the equation 2x4 + 70x2 - 72 = 0 are x = 1 and x = -36.

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