find the equation of the quadratic whose roots are 4 and 3 and the coefficient of the x term is 7

Question

I can't understand how to get my coefficient to 7

Answer 1

(Same as Mark's solution, plus a few details that may be helpful.)

When we know the roots of the quadratic, the function is always of the form

f(x) = a(x - 4)(x - 3)

Expanding, we get

f(x) = a(x² - 7x + 12)

f(x) = ax² -7ax + 12a

So the coefficient of x is -7a.

What value of 'a' will turn the -7 into +7? a = -1, of course.

Plugging in a = -1, we have

f(x) = (-1)*x² + (-1)*(-7x) + (-1)*(12)

or

f(x) = -x² + 7x - 12

Answer 2

Expand the function!

f(x) = a(x - 4)(x - 3)

f(x) = a(x² - 7x + 12)

f(x) = -x² + 7x - 12