Using complete sentences, explain what the discriminant is and what it tells you about the solutions of a quadratic equation. Provide a unique example to back up your explanation.
Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
The discriminant is the value of b^2 - 4ac from the quadratic formula. It is the radicand in the formula.
If the discriminant is a perfect square and positive then you can take a square root that is a real number and your result is two rational numbers: Assume the equation x^2 - 3x + 2 = 0
then b^2 - 4ac = (-3)^2 - 4(1)(2) = 9 - 8 = 1 and there are two rational solutions
If the discriminant is 0, then the radical is 0. and you get a repeated rational solution
Assume that x^2 - 2x + 1 = 0, then b^2 - 4ac = (-2)^2 - 4(1)(1) = 0
the solution is x = -1 a repeated rational number
If the discriminant is positive but not a perfect square, you get two real but irrational solutions Assume x^2 - 4x + 2 = 0, b^2 - 4ac = (-4)^2 - 4(1)(2) = 16 - 8 = 8 and the solutions involves the +- sqrt (8)
If the discriminant is negative you get two complex solutions (since you have a negative under the square root). these solutions on conjugates of each other.
Assume x^2 - x + 1 = 0, b^2 - 4ac = (-1)^2 - 4(1)(1) = 1 - 4 = -3
the solutions are (1 +- sqrt(-3))/2 = (1/2) +- (sqrt 3)/2 i