Question

If a(x) and b(x) are linear functions with one variable, which of the following expressions produces a quadratic function?

Answer 1

Hi,

the answer is A. (ab)(x)

Answer 2

Answer:

Option A (ab)(x) will form the quadratic equation.

Step-by-step explanation:

We have been given that a(x) and b(x) are linear function so we can assume

a(x)= cx+d  and b(x) = ex+f  substituting these values in the given options

In case A let us substitute the values a(x)= cx+d  and b(x) = ex+f  we will get

$(cx+d)(ex+f)$ after simplification we will get $cx(ex+f)+d(ex+f) =cex^2+cxf+dex+df$

This is a quadratic equation because the degree of this equation is 2.

In case B let us substitute the values a(x)= cx+d  and b(x) = ex+f  we will get

$\frac{(cx+d)}{(ex+f)}$ which is itself a simplified from and degree in this case is 1.

Hence, this is not the quadratic equation.

In case C let us substitute the values a(x)= cx+d  and b(x) = ex+f  we will get

$(cx+d)-(ex+f)$ after simplification we will get $cx+d-ex-f$

This is again not a quadratic equation since, degree in this case is 1.

In case D let us substitute the values a(x)= cx+d  and b(x) = ex+f  we will get

$(cx+d)+(ex+f)$ after simplification we will get $cx+d+ex+f$

This is again not a quadratic equation since, degree in this case is 1.

Therefore, Option A (ab)(x) will form the quadratic equation.