Simplify : $$ \sqrt{63}-\sqrt{175}+\sqrt{28} $$ If $$ p(x)=4 x^{3}-6 x^{2}+3 x-14 $$, then find the value of $$ p(-1) $$ and $$ p(0) $$

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Let's address each part of your question step by step.

### Part 1: Simplify $$ \sqrt{63} - \sqrt{175} + \sqrt{28} $$

**Step 1: Simplify Each Square Root**

1. **$$ \sqrt{63} $$**
   $$
   63 = 9 \times 7 \
   \sqrt{63} = \sqrt{9 \times 7} = \sqrt{9} \times \sqrt{7} = 3\sqrt{7}
   $$

2. **$$ \sqrt{175} $$**
   $$
   175 = 25 \times 7 \
   \sqrt{175} = \sqrt{25 \times 7} = \sqrt{25} \times \sqrt{7} = 5\sqrt{7}
   $$

3. **$$ \sqrt{28} $$**
   $$
   28 = 4 \times 7 \
   \sqrt{28} = \sqrt{4 \times 7} = \sqrt{4} \times \sqrt{7} = 2\sqrt{7}
   $$

**Step 2: Combine the Simplified Terms**
$$
\sqrt{63} - \sqrt{175} + \sqrt{28} = 3\sqrt{7} - 5\sqrt{7} + 2\sqrt{7}
$$
$$
= (3 - 5 + 2)\sqrt{7} = 0\sqrt{7} = 0
$$

**Simplified Expression:** $$ 0 $$

---

### Part 2: Evaluate $$ p(-1) $$ and $$ p(0) $$ for $$ p(x) = 4x^3 - 6x^2 + 3x - 14 $$

1. **Evaluate $$ p(-1) $$**
   $$
   p(-1) = 4(-1)^3 - 6(-1)^2 + 3(-1) - 14
   $$
   $$
   = 4(-1) - 6(1) - 3 - 14
   $$
   $$
   = -4 - 6 - 3 - 14 = -27
   $$

2. **Evaluate $$ p(0) $$**
   $$
   p(0) = 4(0)^3 - 6(0)^2 + 3(0) - 14
   $$
   $$
   = 0 - 0 - 0 - 14 = -14
   $$

**Results:**
- $$ p(-1) = -27 $$
- $$ p(0) = -14 $$
Simplify $$ \sqrt{63} - \sqrt{175} + \sqrt{28} $$ to get 0. For the polynomial $$ p(x) = 4x^3 - 6x^2 + 3x - 14 $$: - $$ p(-1) = -27 $$ - $$ p(0) = -14 $$

Simplify :
If , then find the value of and

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Solution

Part 1: Simplify

Part 2: Evaluate and for

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