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

By BYJU'S Exam Prep

Updated on: October 17th, 2023

The zeros of the polynomial x²-√2x-12 are

In the given problem, we can find the zeros by using the given steps:

• Step 1: Set the polynomial equal to zero.
• Step 2: Factor the quadratic expression if possible. If factoring is not possible, we’ll use the quadratic formula. In this case, factoring is not straightforward, so we’ll use the quadratic formula: x = (-b ± √(b2 – 4ac)) / (2a)
• Step 3: Identify the coefficients of the quadratic equation
• Step 4: Apply the quadratic formula
• Step 5: Substitute the coefficients into the quadratic formula

## 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.