The True Statement Is

Welcome to Catalytic, a blog to share questions about Education. This time we will answer questions and at the same time we will address the following questions: True Statements

 

The correct statement is

The True Statement Is

Is known:

  1. x^{2} + 2x - 3 = (x - 3)(x + 1)
  2. x^{2} - 4x + 5 = (x - 5)(x + 1)
  3. x^{2} + 3x - 10 = (x + 5)(x - 2)
  4. 2x^{2} + 7x + 6 = (2x - 3)(x - 2)

 

 

 

The correct statements are (ii) and (iii). (C)

Detailed discussion of the questions above

Quadratic equations are equations with the highest degree variable 2. Quadratic equation have 2 factor So the quadratic equation also has 2 roots.

General Form: \\boxed{ax^{2} + bx + c = 0}

Information:

  • x = variable
  • a and b = coefficients
  • c = constant

From that explanation, let's solve the problem above!

Is known:

  1. x^{2} + 2x - 3 = (x - 3)(x + 1)
  2. x^{2} - 4x + 5 = (x - 5)(x + 1)
  3. x^{2} + 3x - 10 = (x + 5)(x - 2)
  4. 2x^{2} + 7x + 6 = (2x - 3)(x - 2)

Asked:

Correct statement.

Answer:

(i). x^{2} + 2x - 3 = (x - 3)(x + 1)

Obtained that:

x^{2} + 2x - 3

= x^{2} + 3x - x - 3

= x(x + 3) - 1(x + 3)

= (x - 1)(x + 3)

So, it is proven that statement (i) is false.

(ii). x^{2} - 4x + 5 = (x - 5)(x + 1)

Obtained that: x^{2} - 4x + 5

= x^{2} - 5x + x - 5

= x(x - 5) + 1(x - 5)

= (x + 1)(x - 5)

So, it is proven that statement (ii) is true.

(iii). x^{2} + 3x - 10 = (x + 5)(x - 2)

Obtained that:

x^{2} + 3x - 10

= x^{2} + 5x - 2x - 10

= x(x + 5) - 2(x + 5)

= (x - 2)(x + 5)

So, it is proven that statement (iii) is true.

(iv). 2x^{2} + 7x + 6 = (2x - 3)(x - 2)

Obtained that:

2x^{2} + 7x + 6

= 2x^{2} + 3x + 4x + 6

= x(2x + 3) + 2(2x + 3)

= (x + 2)(2x + 3)

So, it is proven that statement (iv) is false.

So, the correct statements are (ii) and (iii).

 

DETAILS Question

Class: 9

Course: Mathematics

Chapter: 9 – Quadratic Equation

 

Keywords: quadratic equation, statement

 

This is the discussion that we have compiled from various sources by the Katalistiwa team. May be useful.

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