What is the value of discriminant?

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. - If b2 – 4ac = 0 then the quadratic function has one repeated real root.

What is the value of its discriminant?

The discriminant is the formula b squared minus 4ac remembering that a, b and c are the coefficients of your quadratic in standard form. It tells you the number of solutions to a quadratic equation. If the discriminant is greater than zero, there are two solutions.

What is the value of discriminant quadratic equation?

If the discriminant value is positive, the quadratic equation has two real and distinct solutions. If the discriminant value is zero, the quadratic equation has only one solution or two real and equal solutions. If the discriminant value is negative, the quadratic equation has no real solutions.

How many solutions if the discriminant is negative?

A Negative Discriminant

The square root of a negative number will involve the imaginary number i. This means that if you have a negative discriminant, you will get two complex solutions.

What is a discriminant example?

Example: Find the discriminant of the quadratic equation 2x² - 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.

How To Determine The Discriminant of a Quadratic Equation

How can we find 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.

What if the discriminant is zero?

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. In this case, we have two real roots. These values of x are the two distinct real roots of the given equation.

How do you find the discriminant of Class 10?

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.

When discriminant is a perfect square?

If the discriminant is a perfect square, then the solutions to the equation are not only real, but also rational. If the discriminant is positive but not a perfect square, then the solutions to the equation are real but irrational.

Which function has a negative discriminant value?

If the discriminant is negative, that means that the roots of the quadratic function are not real numbers.

What is the value of discriminant for the quadratic equation x2?

Summary: The value of the discriminant for the quadratic equation 0 = x + 2 + x² is -7.

What is the value of the discriminant of the quadratic equation ax2 bx c 0?

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 the nature of roots if the discriminant is negative 3?

If the discriminant of the quadratic equation is negative, then the square root of the discriminant will be undefined.

What is the value of discriminant for the quadratic equation x2 2x 3 0?

Answer. The value of discriminant is -16.

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 the discriminant of a cubic equation?

Δ = b² – 4ac. If the discriminant Δ is zero, the equation has a double root, i.e. there is a unique x that makes the equation zero, and it counts twice as a root. If the discriminant is not zero, there are two distinct roots.

How many solutions if the discriminant is positive?

If the discriminant is positive, this means that you have a positive number under the square root in the quadratic formula. This means you will end up with 2 real solutions.

What if discriminant is less than or equal to 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.

How is discriminant formula derived?

Discriminant Formula of a Quadratic Equation

According to the quadratic formula, the roots can be found using x = [-b ± √ (b² - 4ac) ] / [2a]. Here, b² - 4ac is the discriminant D and it is inside the square root. Thus, the quadratic formula becomes x = [-b ± √D] / [2a]. Here D can be either > 0, = 0, (or) < 0.

What is the value of the discriminant b2 − 4ac for the quadratic equation 0 − 2x2 − 3x 8 and what does it mean about the number of real solutions the equation has?

What is the value of the discriminant, b2 − 4ac, for the quadratic equation 0 = −2x2 − 3x + 8, and what does it mean about the number of real solutions the equation has? The discriminant is 73, so the equation has 2 real solutions.

What is the discriminant of 2x2 6x 3 0?

iii) 2x² - 6x + 3 = 0. b² - 4ac is called the discriminant of the quadratic equation and we can decide whether the real roots exist or not based on the value of the discriminant. Hence the equation has no real roots. Hence the equation has two equal real roots.