Factorize and Solve the quadratic equations if possible:
a.  x2 + 3x – 10 = 0
b. 16x2 + 4x + 1 = 0 


Let's factorize and solve the quadratic equations.

### a. \( x^2 + 3x - 10 = 0 \)

We need to find two numbers that multiply to give \(-10\) (the constant term) and add to give \(3\) (the coefficient of \(x\)).

The numbers are \(5\) and \(-2\), since:
- \( 5 \times (-2) = -10 \)
- \( 5 + (-2) = 3 \)

Thus, we can rewrite the quadratic equation as:
\[
x^2 + 5x - 2x - 10 = 0
\]
Now, factor by grouping:
\[
x(x + 5) - 2(x + 5) = 0
\]
Factor out the common factor \((x + 5)\):
\[
(x + 5)(x - 2) = 0
\]
Now, solve for \(x\) by setting each factor equal to zero:
\[
x + 5 = 0 \quad \text{or} \quad x - 2 = 0
\]
\[
x = -5 \quad \text{or} \quad x = 2
\]

**Solution for part a:** \( x = -5 \) or \( x = 2 \)

---

### b. \( 16x^2 + 4x + 1 = 0 \)

This is a perfect square trinomial because it can be factored as:
\[
(4x + 1)(4x + 1) = 0 \quad \text{or} \quad (4x + 1)^2 = 0
\]
Now, solve for \(x\):
\[
4x + 1 = 0
\]
\[
4x = -1
\]
\[
x = -\frac{1}{4}
\]

**Solution for part b:** \( x = -\frac{1}{4} \) (double root)

---

### Summary of Solutions:
- **Part a:** \( x = -5 \) or \( x = 2 \)
- **Part b:** \( x = -\frac{1}{4} \) (double root)

Would you like more details on the factoring process or the nature of the roots? 

Here are 5 related questions:
1. How do we know if a quadratic can be factorized?
2. What is the quadratic formula, and how can it be applied here?
3. What are the methods for solving non-factorable quadratic equations?
4. What are perfect square trinomials, and how do they simplify solving quadratics?
5. How does the discriminant help in determining the nature of roots?

**Tip:** Always check if a quadratic is a perfect square trinomial before factoring! It can save time when solving.

Factorize and Solve the quadratic equations if possible:
 a.  x^2 + 3x – 10 = 0
 b. 16x^2 + 4x + 1 = 0

Learn how to factorize and solve quadratic equations like x^2 + 3x - 10 and 16x^2 + 4x + 1 with a detailed, step-by-step solution. Explore factoring techniques and recognize perfect square trinomials. Suitable for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation