If the discriminant of an equation is negative, which of the following is true of the equation?A.It has two complex solutions.B.It has one real solution.C.It has two real solutions.SUBMITarrow_backPREVIOUS
Question
If the discriminant of an equation is negative, which of the following is true of the equation?A.It has two complex solutions.B.It has one real solution.C.It has two real solutions.SUBMITarrow_backPREVIOUS
Solution
The correct answer is A. It has two complex solutions.
Here's why:
The discriminant of a quadratic equation is found in the formula ax^2 + bx + c = 0, and it's calculated as b^2 - 4ac.
The discriminant tells us about the nature of the roots of the equation:
- If the discriminant is positive, we have two distinct real roots.
- If the discriminant is zero, we have exactly one real root (or a repeated real root).
- If the discriminant is negative, we have two complex roots.
So, if the discriminant of an equation is negative, the equation has two complex solutions.
Similar Questions
If a quadratic equation has a discriminant that equals zero, which of the following statements is always true?
Consider only the discriminant, b2 - 4ac, to determine whether one real-number solution, two different real-number solutions, or two different imaginary-number solutions exist.-9 - 5x2 = 4x - 12Group of answer choicesOne real solutionTwo different imaginary-number solutionsTwo different real-number solutionsNext
Consider the following equation:−3𝑥2−2𝑥−5=0First calculate the discriminant.Δ= How many real solutions does this equation have? Two real solutions One repeated solution No real solutions
Using the discriminant, determine how many real solutions each equation has.No RealSolutions One RealSolution Two RealSolutions0=2x2+x+10=2𝑥2+𝑥+1 −2=−4x2−12x−2=−4𝑥2−12𝑥 12=6x2+x12=6𝑥2+𝑥 0=−34x2−12x−48
For a quadratic equation ax2 + bx + c = 0, which of the following statements is necessarily true, if the roots of the equation are opposite in sign, the root with the greater absolute value being negative?
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.