When the value of the discriminant is greater than zero then the given quadratic equation has what kind of roots?

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. In this case, we have two real roots.

When you find the discriminant of an equation and the value is greater than zero it means the equation has?

The discriminant can be positive, zero, or negative, and this determines how many solutions there are to the given quadratic equation. A positive discriminant indicates that the quadratic has two distinct real number solutions. A discriminant of zero indicates that the quadratic has a repeated real number solution.

When the value of the discriminant is greater than zero then?

If a>0 the graph will be an upward parabola and it will cut the x-axis at two distinct points indicating real and distinct roots. For real and distinct roots, the value of the discriminant is greater than zero.

When discriminant is zero then roots are?

Clearly, the discriminant of the given quadratic equation is zero. Therefore, the roots are real and equal.

What can you say about the roots of a quadratic equation if its discriminant is greater than zero but is a perfect square?

The discriminant is 0, so the equation has a double root. 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.

How To Determine The Discriminant of a Quadratic Equation

When the value of the discriminant is greater than zero and a perfect square What does this tell us with regards to the nature of the roots of the equation?

We have calculated that \(Δ > 0\) and is a perfect square, therefore we can conclude that the roots are real, unequal and rational. We have calculated that \(Δ = 0\) therefore we can conclude that the roots are real and equal.

How many words are there if the discriminant of a quadratic equation is greater than 0?

If the discriminant is greater than zero or positive, then there are 2 real solutions. If the discriminant is equal to zero, then there is one real solution. If the discriminant is negative or less than zero, there are 2 imaginary solutions.

How do you tell if roots are rational or irrational?

If the discriminant is positive and is a perfect square (ex. 36,121,100,625 ), the roots are rational. If the discriminant is positive and is not a perfect square (ex. 84,52,700 ), the roots are irrational.

What is the discriminant of a quadratic equation is 0?

When the discriminant of a quadratic equation is 0 that means it has real and equal roots.

What happens when 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.

Which of the following is the nature of the roots of the quadratic equation if the value of its discriminant is zero?

Answer : If the value of the discriminant is 0, the roots of a quadratic equation are real and equal.

Which of the following is the nature of the roots of the quadratic equation if the value of its discriminant is negative?

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

How many solutions and what type of solutions does a quadratic equation have if the value of the discriminant is a positive perfect square?

If the discriminant is a positive number, then there are 2 real solutions. This means that the graph of the parabola interepts the x-axis at 2 distinct points . If the discriminant is positive and also a perfect square like 64, then there are 2 real rational solutions.

How many solutions does the discriminant have greater than zero?

If the discriminant is greater than zero, there are two solutions. If the discriminant is less than zero, there are no solutions and if the discriminant is equal to zero, there is one solution.

When the discriminant is zero how many real solutions does the quadratic equation have?

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.

Is the discriminant of an equation is positive which of the following is true of the equation?

it has one real solution. Summary: If the discriminant of an equation is positive, then it has two real solutions.

Which of the following is the nature of the roots of the quadratic equation if the value of its discriminant is positive and a perfect square?

Clearly, the discriminant of the given quadratic equation is positive and a perfect square. Therefore, the roots of the given quadratic equation are real, rational and unequal.

Which quadratic equation has irrational roots?

ax2 + bx + c = 0 where, the coefficients a, b and c are real. Let p + √q (where p is rational and √q is irrational) be a surd root of equation ax2 + bx + c = 0. Then the equation ax2 + bx + c = 0 must be satisfied by x = p + √q.

What are the types of roots in quadratic equation?

There are three types of roots of a quadratic equation ax2+bx+c=0 a x 2 + b x + c = 0 : Real and distinct roots. Real and equal roots. Complex roots.

What are irrational roots?

Real numbers have two categories: rational and irrational. If a square root is not a perfect square, then it is considered an irrational number. These numbers cannot be written as a fraction because the decimal does not end (non-terminating) and does not repeat a pattern (non-repeating).

How many solutions does a quadratic equation have 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.

How many real solutions does a quadratic equation have if its discriminant has a value that is a positive B negative and C zero?

If you get a positive number, the quadratic will have two unique solutions. If you get 0, the quadratic will have exactly one solution, a double root. If you get a negative number, the quadratic will have no real solutions, just two imaginary ones.

What is a irrational solution?

Irrational solutions - An irrational number is a number that cannot be written as a fraction. In these cases, the equation does not have a perfect square, but the solutions can be found by taking the square root and rounding.

What is the nature of the quadratic equation if the discriminant is less than zero?

When discriminant is equal to zero, the roots are equal and real. When discriminant is less than zero, the roots are imaginary.