Two questions with quadratics a (x2 + b x + c = 0) and perfect squares.
1.) Write a quadratic function by using the zeros 3 and -4.
2.) x^2+7x+c What would c have to be to get a perfect square?
1) recall that a quadratic in the form x^2 + bx + c = 0 can often be factored in the form (x+n)(x+m) = 0, where x = -n and x = -m are the roots.
For this reason, if we know the roots (in this case, 3 and -4), we can write the factored form of the quadratic:
(x-3)(x+4) = 0 <--- notice the signs are oposite of their roots.
2) x^2 + 7x + c ... let's pretend like we're completing the square to find the value for c:
x^2 + 7x ... taking 7, dividing it by 2, then squaring that, we get, 49/4 ... if we were completing the sqare, we would add and subtract 49/4 and then use the 49/4 to factor x^2 + 7x + c, therefore:
c = 49/4