What are the roots of the equattorit $$ x^{2}-3 x-10=0 $$ Answer $$ \frac{3 \pm \sqrt{31}}{2} $$ Submit Answer 2 and - 5 $$ \frac{-3 \pm \sqrt{31}}{2} $$ 5 and -2 Copyright O2025 DeltaMath.com All Rights Reserved. Terms \& Policies

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UpStudy AI · Accepted Answer

**Step 1:** Write down the quadratic equation  
$$
x^2 - 3x - 10 = 0
$$

**Step 2:** Identify the coefficients  
$$
a = 1, \quad b = -3, \quad c = -10.
$$

**Step 3:** Use the quadratic formula  
$$
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.
$$

**Step 4:** Substitute the coefficients into the formula  
$$
x = \frac{-(-3) \pm \sqrt{(-3)^2 - 4(1)(-10)}}{2(1)} = \frac{3 \pm \sqrt{9 + 40}}{2}.
$$

**Step 5:** Simplify under the square root  
$$
9 + 40 = 49,
$$
so  
$$
x = \frac{3 \pm \sqrt{49}}{2} = \frac{3 \pm 7}{2}.
$$

**Step 6:** Solve for the two roots  
For the positive case:  
$$
x = \frac{3 + 7}{2} = \frac{10}{2} = 5.
$$  
For the negative case:  
$$
x = \frac{3 - 7}{2} = \frac{-4}{2} = -2.
$$

**Final Answer:** The roots of the equation are $$5$$ and $$-2$$.
The roots of the equation $$ x^{2} - 3x - 10 = 0 $$ are $$5$$ and $$-2$$.

What are the roots of the equattorit \[ x^{2}-3 x-10=0 \] Answer \( \frac{3 \pm \sqrt{31}}{2} \) Submit Answer 2 and - 5 \( \frac{-3 \pm \sqrt{31}}{2} \) 5 and -2 Copyright O2025 DeltaMath.com All Rights Reserved. Terms \& Policies

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