Choose the quadratic equation with a leading coefficient of one that has a solution -for and 7

x² -3x -28 = 0

Step-by-step explanation:

If the roots are -4 and 7, the factors are ...

... (x -(-4))·(x -7) = (x +4)(x -7)

and the equation with those zeros is ...

... (x +4)(x -7) = 0 = x² -3x -28

Comment on such questions

If "a" is a root/zero/solution, then (x-a) is a factor of the quadratic expression whose value is zero. A quadratic will have 2 roots, so we can call them "p" and "q" and write the factored form as

... (x -p)(x -q) = 0

Expanding gives ...

... x² -(p+q)x +pq = 0

Comparing this to the generic equation ...

... ax² +bx +c = 0

we see that when the leading coefficient (a) is 1, then b=-(p+q), the opposite of the sum of the solutions; and c=pq, the product of the solutions. So, when you are given the two solutions as being -4 and +7, you can write the equation as

... x² -(-4+7)x +(-4)(7) = 0

... x² -3x -28 = 0