Question

What is the value of a in the equation 24x² + 113x + 39 = (ax + b) (cx + d)?

Answer 1

The value of 'a' in the equation 24x² + 113x + 39 = (ax + b) (cx + d) is not uniquely determinable without additional constraints, but the product of 'a' and 'c' must be 24.

Step-by-step explanation:

To find the value of a in the equation 24x² + 113x + 39 = (ax + b) (cx + d), we need to match the coefficients of the quadratic on the left to the product of binomials on the right. Since the coefficient of x² in the original equation is 24, this must be the result of multiplying a and c from the binomials. By convention, we often assume the leading coefficient a is 1 in the first binomial unless we have additional constraints, so it's more likely that c = 24 and a = 1, but without more information, we cannot precisely determine the values of a and c. We know for certain that the product of a and c is 24.

Answer 2

The value of a in the equation 24x² +113x+39=(ax+b)(cx+d) is a=3.

Step-by-step explanation:

To find the value of a, let's first expand the right side of the equation (ax+b)(cx+d):

(ax+b)(cx+d)=acx² +(ad+bc)x+bd

Now, we can equate the coefficients of the expanded form with the given quadratic equation 24x²+113x+39:

ac=24

ad+bc=113

bd=39

Since the coefficient ac is 24, and a and c are integers, the possibilities for a and c are (a,c)=(1,24),(2,12),(3,8),(4,6),(6,4),(8,3),(12,2),(24,1).

Trying these possibilities, we find that a=3 and c=8 satisfy the conditions. Therefore, the value of a is 3.