The discriminant of a quadratic equation $$ax^2+bx+c=0$$ is a number, indicated with the letter $$D$$ (in some texts the Greek letter $$\Delta$$ is used) whose value is calculated as follows: $$D=b^2-4ac$$Example $$$x^2+3x-10=0 \rightarrow D=3^2-4 \cdot 1 \cdot (...
to solve the quadratic equationax2+bx+c= 0(a≠ 0) by completing the square, it can be transformed intoa(x+b2a)2=b24ac4a,i.e.(x+b2a)2=b24ac4a2.#According to the definition of square root, whenb2 4ac≥ 0, the equation has real roots; whenb2 4ac< 0, the equation has no real...
The discriminant of a quadratic equation equals b2 - 4a, the radicand in theQuadratic Formula. It allows you to determine the nature of the roots of a quad-ratic equation without actually solving for them.1. Ifb^2-4ac0 , there are two real, unequal roots.When b2 - 4ac is a perfect...
the vertex, in particular, must have a non-negative y coordinate. The x-coordinate of the vertex is x = 2b/15a. (If you do not know why that is, see NOTE 1 below.) Thus the y-coordinate of the vertex is y = 15a(2b/15a)² - 4b(2b/15a) + 4c = 4b²/15a - 8b²/15a...
they have been important in the physics ofacceleratedmotion, such as free fall in a vacuum. The general quadratic equation in one variable isax2+bx+c= 0, in whicha, b,andcare arbitrary constants (or parameters) andais not equal to 0. Such anequationhas two roots (not necessarily distinc...
In the last example, we will draw a correlation between the number and type of solutions to a quadratic equation of the form 0=ax2+bx+c0=ax2+bx+c and its corresponding graph for y=ax2+bx+cy=ax2+bx+c. (Remember, the x-intercepts correspond to the solutions of the equation 0=ax2...
Chinese English Pinyin Dictionary Search with English, Pinyin, or Chinese characters. Powered byCC-CEDICT 判别式Trad.判別式 pàn bié shì discriminant (e.g. b^2-4ac in the formula for the root of a quadratic equation)
in this equation k2 - 6k - 7 = 0 a = 1, b = -6, c = -7 the discriminant of the quadratic equation is Δ =b2 - 4ac = (-6)2 - 4 * 1 * (-7) = 36 + 28 = 64 > 0 the equation will have two different solution k = (-b...
Using the Discriminant to Determine the Nature of Roots of a Quadratic Equation Step 1: Identify a, b, and c in the quadratic equation {eq}ax^2 + bx + c = 0 {/eq}. Step 2: Substitute the values found in step 1 into the formula for the discriminant, {eq}\Delta = b^2 - ...
4.Remember how the discriminant determines the number of solutions of a quadratic equation? 5."Unfortunately, many of these critics can get away with just suggesting that bombing more, or being less discriminant in how we approach that, would make a difference," he said. 6.The algorithm based...