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

The given quadratic equation is 3 – 4x = -6×2. The standard quadratic equation is the form ax2 + bx + c= 0. Therefore, the discriminant of the quadratic equation 3 – 4x = -6×2 is – 56.


What is the discriminant of the quadratic equation 2x 5x?

The given quadratic equation is 2x + 5×2 = 1. Discriminant form of the quadratic equation . As the quadratic equation in the form. Therefore, the discriminant of the quadratic equation 2x + 5×2 = 1 is 24.


How do you find the discriminant of 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.

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What is a discriminant in quadratic equation?

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.


What is the nature of the roots if the value of the discriminant is?

When discriminant is greater than zero, the roots are unequal and real. When discriminant is equal to zero, the roots are equal and real. When discriminant is less than zero, the roots are imaginary. Subject : Math. Topic : Algebra 2.


What are the nature of roots?

Answer: The nature of roots simply means the category in which the roots are falling upon. The roots may be imaginary, real, unequal or equal. If the discriminate is negative, the roots will be imaginary.


What is the value of the discriminant of the quadratic equation 2 =- 8x 8 and what does its value mean about the number of real number solutions the equation has?

What is the value of the discriminant of the quadratic equation. 0 2×2 −8x +8 = 0 , and what does its value mean about the number of real number solutions the equation has? The discriminant = 0, which means there are 0 real number solutions.


Which of the following formula can be used to determine the sum of the roots of a quadratic equation?

The sum of the roots of a quadratic equation is equal to the negation of the coefficient of the second term, divided by the leading coefficient. The product of the roots of a quadratic equation is equal to the constant term (the third term), divided by the leading coefficient.


How do you find the discriminant and nature of roots?

The discriminant is defined as Δ=b2−4ac. This is the expression under the square root in the quadratic formula. The discriminant determines the nature of the roots of a quadratic equation. The word ‘nature’ refers to the types of numbers the roots can be — namely real, rational, irrational or imaginary.

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What is the value of the discriminant b2?

A quadratic equation is an equation in the form ax2 + bx + c = 0 where a ≠ 0. For the quadratic equation ax2 + bx + c = 0, the expression b2 – 4ac is called the discriminant. The value of the discriminant shows how many roots f(x) has: – If b2 – 4ac > 0 then the quadratic function has two distinct real roots.


How many roots are there if the discriminant is less than zero?

If the discriminant of a quadratic function is less than zero, that function has no real roots, and the parabola it represents does not intersect the x-axis.


What is discriminant Class 11?

The discriminant formula is used to find the number of solutions that a quadratic equation has. In algebra, the discriminant is the name given to the expression that appears under the square root (radical) sign in the quadratic formula.


What is quadratic equation for class 10th?

A quadratic equation in the variable x is an equation of the form ax2 + bx + c= 0, where a, b, c are real numbers, a * 0. For example, 2×2 + x – 300 = 0 is a quadratic equation. Similarly, 2×2 – 3x + 1 = 0, 4x – 3×2 + 2 = 0 and 1 – x2 + 300 = 0 are also quadratic equations.


How do you find the discriminant of a root?

b2 – 4ac = (3)2 – 4(-1)(-3) = 9 – 12 = -3. When the discriminant is greater than 0, there are two distinct real roots. When the discriminant is equal to 0, there is exactly one real root. When the discriminant is less than zero, there are no real roots, but there are exactly two distinct imaginary roots.


Why does the discriminant work?

The discriminant is the term underneath the square root in the quadratic formula and tells us the number of solutions to a quadratic equation. If the discriminant is positive, we know that we have 2 solutions. If it is negative, there are no solutions and if the discriminant is equal to zero, we have one solution.

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What are equal roots?

A quadratic equation has equal roots iff its discriminant is zero. A quadratic equation has equal roots iff these roots are both equal to the root of the derivative.


What is quadratic standard form?

Standard Form. The quadratic function f(x) = a(x – h)2 + k, a not equal to zero, is said to be in standard form. If a is positive, the graph opens upward, and if a is negative, then it opens downward. The line of symmetry is the vertical line x = h, and the vertex is the point (h,k).


How do you find the alpha and beta of a quadratic equation?

α+β=−baandαβ=ca. From these formulas, we can also find the value of the sum of the squares of the roots of a quadratic without actually solving the quadratic.


What is the value of the discriminant of the quadratic equation and what does its value mean about the number of real number solutions the equation has?

If the discriminant is greater than 0, the quadratic equation has 2 real solutions. If the discriminant is equal to 0, the quadratic equation has 1 real solution. If the discriminant is less than 0, the quadratic equation has 0 real solutions.


What are the solutions to the quadratic equation 6 x2 10x?

In simplest radical form, what are the solutions to the quadratic equation 6 = x2 – 10x? Summary: In simplest radical form, the solutions to the quadratic equation 6 = x2 – 10x are 5 + √31, and 5 – √31.


What is the value of the discriminant of the quadratic equation − 1 5×2 − 2x?

What is the value of the discriminant of the quadratic equation -1=5×2-2x , and what does its value mean about the number of real number solutions the equation has? The discriminant is equal to −16, which means the equation has no real number solutions.

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