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Chapter 7: Q 131. (page 833)

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

Expert verified

The value ofmandnisrole="math" localid="1649484902769" (-b+b2-4c)2and(-b-b2-4c)2.

Step by step solution

01

Step 1. Given information  

Given trinomial isx2+bx+cand the given factorize form is(x+m)(x+n).

02

Step 2. Find the value of m and n

Equate the given trinomial with the factorized form .

Then evaluate mand nby equating the coefficient of like terms from both sides.

By comparing like terms.

m+n=band mn=c

Use this two equations and the formula.(m-n)2=(m+n)2-4mn

To find mand n in termsof band c.

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