Chapter 7: Q 131. (page 833)

Many trinomials of the form $x^{2} + b x + c$ factor into the product of two binomials $(x + m) (x + n)$ . Explain how you find the values of $m$ and $n$ .

Short Answer

Expert verified

The value of $m$ and $n$ isrole="math" localid="1649484902769" $\frac{(- b + \sqrt{b^{2} - 4 c})}{2}$ and $\frac{(- b - \sqrt{b^{2} - 4 c})}{2}$ .

Step by step solution

Step 1. Given information

Given trinomial is $x^{2} + b x + c$ and the given factorize form is $(x + m) (x + n)$ .

Step 2. Find the value of m and n

Equate the given trinomial with the factorized form .

Then evaluate $m$ and $n$ by equating the coefficient of like terms from both sides.

By comparing like terms.

$m + n = b$ and $m n = c$

Use this two equations and the formula. ${(m - n)}^{2} = {(m + n)}^{2} - 4 m n$

To find $m$ and n in termsof $b$ and $c$ .

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Many trinomials of the form $x^{2} + b x + c$ factor into the product of two binomials $(x + m) (x + n)$ . Explain how you find the values of $m$ and $n$ .

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the value of m and n

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Many trinomials of the form x2+bx+cfactor into the product of two binomials (x+m)(x+n). Explain how you find the values ofmandn.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the value of m and n

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

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Study anywhere. Anytime. Across all devices.

Many trinomials of the form $x^{2} + b x + c$ factor into the product of two binomials $(x + m) (x + n)$ . Explain how you find the values of $m$ and $n$ .