discriminant meaning

discriminant, in mathematics, a parameter of an object or system calculated as an aid to its classification or solution. In the case of a quadratic equation ax2 + bx + c = 0, the discriminant is b2 − 4ac; for a cubic equation x3 + ax2 + bx + c = 0, the discriminant is a2b2 + 18abc − 4b3 − 4a3c − 27c2.

What is discriminant example?

Example: Find the discriminant of the quadratic equation 2×2 – 3x + 8 = 0. Comparing the equation with ax2 + bx + c = 0, we get a = 2, b = -3, and c = 8. So the discriminant is, Δ OR D = b2 − 4ac = (-3)2 – 4(2)(8) = 9 – 64 = -55.

What is the discriminant of 76?

The discriminant is 76, which is positive. This means that there are two real solutions.

How do you calculate the discriminant?

The discriminant is the part of the quadratic formula underneath the square root symbol: b²-4ac. The discriminant tells us whether there are two solutions, one solution, or no solutions.

Example
a = 6 a=6. a=6.b = 10 b=10 b=10.c = − 1 c=-1 c=−1.

What is discriminant Class 10?

Discriminant. For a quadratic equation of the form ax2+bx+c=0, the expression b2−4ac is called the discriminant, (denoted by D), of the quadratic equation. The discriminant determines the nature of roots of the quadratic equation based on the coefficients of the quadratic equation.

What is the discriminant of the quadratic equation 3 4x =- 6×2?

The discriminant of the quadratic equation 3 – 4x = -6×2 is -56.

What is the discriminant of 2×2 4x 3 0?

The discriminant of the quadratic equation 2×2−4x+3=0 is. 2.

What is the discriminant of 3×2 10x =- 2?

The discriminant of is 76.

What is the axis of symmetry?

The axis of symmetry is the vertical line that goes through the vertex of a parabola so the left and right sides of the parabola are symmetric. To simplify, this line splits the graph of a quadratic equation into two mirror images.

What is discriminant Delta?

The discriminant of a quadratic polynomial, denoted Δ, is a function of the coefficients of the polynomial, which provides information about the properties of the roots of the polynomial.

What is quadratic standard form?

The standard form of a quadratic function is f(x)=a(x−h)2+k. The vertex (h,k) is located at h=–b2a,k=f(h)=f(−b2a).

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