The Zeros of the Polynomial x²-√2x-12 are

The Zeros of the Polynomial x²-√2x-12 are

Solution:

To find the zeros of the polynomial x² – √2x – 12, we need to solve the equation x²– √2x – 12 = 0.

We can use the quadratic formula to find the solutions. The quadratic formula states that for an equation of the form ax² + bx + c = 0, the solutions (zeros) are given by:

x = (-b ± √(b² – 4ac)) / (2a)

In our case, a = 1, b = -√2, and c = -12.

Substituting these values into the quadratic formula, we have:

x = (-(-√2) ± √((-√2)² – 4(1)(-12))) / (2(1))

Simplifying further:

x = (√2 ± √(2 – 4(-12))) / 2 x = (√2 ± √(2 + 48)) / 2 x = (√2 ± √50) / 2

Now, we can simplify the expression under the square root:

x = (√2 ± √(25 ×2)) / 2 x = (√2 ± 5√2) / 2

We can factor out √2 from the numerator:

x = (√2(1 ± 5)) / 2

Finally, we have the two solutions (zeros) of the polynomial:

• x₁ = (√2(1 + 5)) / 2 = (6√2) / 2 = 3√2
• x₂ = (√2(1 – 5)) / 2 = (-4√2) / 2 = -2√2

Therefore, the zeros of the polynomial x² – √2x – 12 are x = 3√2 and x = -2√2.

Answer:

The Zeros of the Polynomial x²-√2x-12 are x = 3√2 and x = -2√2

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