Question

If (ax + 2)(bx + 7) = 15(x*2) + cx + 14 for all values of

Answer 1

If (ax + 2)(bx + 7) = 15(x $*$ 2) + cx + 14 for all values of x, and a + b = 8 then the two possible values for c is 31 and 41.

What is meant by linear equation?

A linear equation is an algebraic equation with only a constant and a first-order (linear) term of the form y = mx + b, where m is the slope and b is the y-intercept. The above is sometimes referred to as a "linear equation of two variables," where y and x are the variables.

Let the equation be

(ax + 2)(bx + 7) = 15$x^2$ + cx + 14

(ax + 2)(bx + 7) = ab$x^2$ + 7ax + 2bx + 14 = ab$x^2$ + (7a + 2b) + 14

On comparing both equations

ab = 15     ------ (1)

7a + 2b = c   -------(2)

Also, it is given that a + b = 8  --------(3)

From equations (1) and (3) it can be observe that either a or b equal to 3 or 5

From equation (2),

When a = 3 and b = 5, then c = 7(3) + 2(5) = 21 + 10 = 31

When a = 5 and b = 3, then c = 7(5) + 2(3) = 35 + 6 = 41

Therefore, the correct answer is option D) 31 and 41

To learn more about linear equation, refer to:

brainly.com/question/2030026

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