12.0k views
20 votes
If the discriminant = 17, determine the number of solutions and types of solutions for the quadratic equation.

(A) one rational solution
(B) Two rational Solutions
(C) Two Irrational Solution

User Ragav Y
by
4.5k points

2 Answers

3 votes

Final answer:

The discriminant value of 17 for a quadratic equation indicates two distinct, real, and irrational solutions, as the discriminant is positive and not a perfect square, implying the roots involve the square root of 17.

Step-by-step explanation:

If the discriminant of a quadratic equation is equal to 17, this means that the equation will have two distinct real and irrational solutions. The general form of a quadratic equation is ax² + bx + c = 0, and the discriminant can be found by using the formula b² - 4ac. When the discriminant is positive and not a perfect square, it indicates two irrational roots which are not rational numbers. Therefore, the correct option is:

(C) Two Irrational Solutions

The quadratic equation mentioned with a = 1.00, b = 10.0, and c = -200 can be solved using the quadratic formula, which is -b ± √b² - 4ac over 2a. Since the discriminant is positive and not a perfect square, applying the formula will yield two complex numbers that involve square roots of 17, thus validating that they are indeed irrational.

User Daaawx
by
4.1k points
11 votes
the answer is B sorry if i m wrong
User Wjin
by
5.0k points