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Applied Calculus

7th Edition
Waner + 1 other
ISBN: 9781337291248

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Section
BuyFindarrow_forward

Applied Calculus

7th Edition
Waner + 1 other
ISBN: 9781337291248
Textbook Problem

In Exercises 31–48, (a) factor the given expression, and (b) set the expression equal to zero and solve for the unknown (x in the odd-numbered exercises and y in the even-numbered exercises.)

6 x 2 + 13 x + 6

(a)

To determine

To calculate: The factors of the expression 6x2+13x+6.

Explanation

Given information:

The expression, 6x2+13x+6.

Formula used:

Steps to calculate the factors of quadratic equation ax2+bx+c by trial and error method,

Step1: Factor ax2 as (a1x)(a2x) with a1 positive.

Step2: Factor c as c1c2.

Step 3: Check if ax2+bx+c=(a1x±c1)(a2x±c2)

If yes, then (a1x±c1)(a2x±c2) are the factors.

Step 4: If not, try other factorization of ax2 and c and repeat all the steps.

The distributive law,

(a±b)c=ac±bc

Where, a, b and c are any real numbers.

Calculation:

Consider the expression,

6x2+13x+6

Factor of 6x2 are (2x)(3x),(3x)(2x), (6x)(x) and (x)(6x)

(b)

To determine

To calculate: The value of x when the expression 6x2+13x+6 is equal to zero.

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