Write a quadratic equation in standard form that has two solutions, -9 and -7 .
$=0$
(The leading coefficient must be 1.)
Final Answer: The quadratic equation in standard form that has two solutions, -9 and -7, is \(\boxed{x^2 + 16x + 63 = 0}\).
Step 1 :The standard form of a quadratic equation is \(ax^2 + bx + c = 0\).
Step 2 :We are given the roots of the equation as -9 and -7, and we want the leading coefficient (a) to be 1.
Step 3 :We can use the fact that the sum of the roots is equal to \(-b/a\) and the product of the roots is equal to \(c/a\).
Step 4 :Given that the roots are -9 and -7, we can find the values of b and c by using the sum and product of the roots.
Step 5 :The sum of the roots is -9 + -7 = -16, so \(b = -(-16) = 16\).
Step 6 :The product of the roots is -9 * -7 = 63, so \(c = 63\).
Step 7 :Substituting a, b, and c into the standard form of the quadratic equation, we get \(x^2 + 16x + 63 = 0\).
Step 8 :Final Answer: The quadratic equation in standard form that has two solutions, -9 and -7, is \(\boxed{x^2 + 16x + 63 = 0}\).