If a quadratic equation has a discriminant that equals zero, which of the following statements is always true?
Question
If a quadratic equation has a discriminant that equals zero, which of the following statements is always true?
Solution
The quadratic equation will have exactly one real solution. This is because the discriminant (b² - 4ac) of a quadratic equation (ax² + bx + c = 0) determines the nature of the roots of the equation. If the discriminant equals zero, it means that the equation has exactly one real root (also known as a repeated root). This is because the roots of a quadratic equation are given by the formula (-b ± √(b² - 4ac)) / 2a. If the discriminant is zero, then the square root term disappears, and the equation has only one solution: -b / 2a.
Similar Questions
In the quadratic formula, x=−b±b2−4ac√2a𝑥=−𝑏±𝑏2−4𝑎𝑐2𝑎, the discriminant is the value of which portion of the formula?Question 3Select one:
A quadratic equation ax2 + bx + c = 0, such that a + b + c = 0, has equal roots. Which of the following statements must be true?b = 2aa = 4ca2 + b2 = c2a = c
What is the discriminant of the quadratic equation minus, x, squared, plus, 6, x, minus, 6, equals, 0−x 2 +6x−6=0?Answer
The number of unique zeroes of a quadratic polynomial with value of discriminant equal to zeroSelect an answerAexactly 1Bexactly 3Cexactly 2DNone of these
What is the discriminant of the quadratic equation x, squared, minus, 9, x, minus, 3, equals, 0x 2 −9x−3=0?
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.