Write a quadratic equation that has integer coefficients and has solutions and .
E) None of the above

Question

Write a quadratic equation that has integer coefficients and has solutions  and  .
E) None of the above

Quizplus · Accepted Answer

Since the solutions are given in the form of irrational numbers, their conjugates will also be solutions. Thus, the quadratic equation will have four solutions, which means it can be factored as a product of two quadratics with integer coefficients. Using the given solutions, we can write them as:

(x - 11eb69da_9f30_6d4e_af94_7756bdd23a64_TB8311_11)(x - 11eb69da_9f30_6d4f_af94_5b2dc21dbbc2_TB8311_11)(ax + b)(cx + d)

Expanding this expression and comparing it with the general form of a quadratic equation (ax^2 + bx + c), we can find the values of a, b, c, and d to be integers. The resulting quadratic equation is:

x^2 - 23688x + 182026210213923626830111776070176416224_TB8311_11

which has integer coefficients and the given solutions. The correct answer is D.

Write a Quadratic Equation That Has Integer Coefficients and Has