Given $$ h(x)=x^{4}-36 x^{2}+275 $$ (a) Evaluate $$ h(\sqrt{11}) $$ (b) Evaluate $$ h(-\sqrt{11}) $$ (c) Solve $$ h(x)=0 $$ Write your answers in exact form.

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**(a) Evaluate $$ h(\sqrt{11}) $$:**

1. Substitute $$ x = \sqrt{11} $$ into the function:
   $$
   h(\sqrt{11}) = (\sqrt{11})^4 - 36(\sqrt{11})^2 + 275
   $$
2. Compute the powers:
   - $$ (\sqrt{11})^2 = 11 $$
   - $$ (\sqrt{11})^4 = ( (\sqrt{11})^2 )^2 = 11^2 = 121 $$
3. Substitute the computed values:
   $$
   h(\sqrt{11}) = 121 - 36(11) + 275
   $$
4. Simplify:
   $$
   h(\sqrt{11}) = 121 - 396 + 275 = (121 + 275) - 396 = 396 - 396 = 0
   $$

So, 
$$
h(\sqrt{11}) = 0.
$$

---

**(b) Evaluate $$ h(-\sqrt{11}) $$:**

1. Notice that $$ h(x) $$ is an even function because it contains only even powers of $$ x $$. Hence,
   $$
   h(-\sqrt{11}) = h(\sqrt{11}) = 0.
   $$

---

**(c) Solve $$ h(x) = 0 $$:**

1. Start with:
   $$
   x^4 - 36x^2 + 275 = 0.
   $$
2. Let $$ u = x^2 $$. Then the equation becomes:
   $$
   u^2 - 36u + 275 = 0.
   $$
3. Solve the quadratic equation in $$ u $$. The discriminant is:
   $$
   \Delta = 36^2 - 4 \cdot 1 \cdot 275 = 1296 - 1100 = 196.
   $$
4. Find $$ u $$ using the quadratic formula:
   $$
   u = \frac{36 \pm \sqrt{196}}{2} = \frac{36 \pm 14}{2}.
   $$
5. This gives two solutions:
   $$
   u = \frac{36 + 14}{2} = 25 \quad \text{and} \quad u = \frac{36 - 14}{2} = 11.
   $$
6. Recall that $$ u = x^2 $$. Therefore, for $$ u = 25 $$:
   $$
   x^2 = 25 \implies x = \pm 5.
   $$
7. And for $$ u = 11 $$:
   $$
   x^2 = 11 \implies x = \pm \sqrt{11}.
   $$

Thus, the solutions are:
$$
x = \pm 5, \quad x = \pm \sqrt{11}.
$$
**(a) $$ h(\sqrt{11}) = 0 $$** **(b) $$ h(-\sqrt{11}) = 0 $$** **(c) $$ x = \pm 5 $$ or $$ x = \pm \sqrt{11} $$**

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(b) Evaluate
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