## Is discriminant positive or negative?

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 negative discriminant indicates that neither of the solutions are real numbers.

When x be real then, the sign of the quadratic expression ax^2 + bx + c is the same as a, except when the roots of the quadratic equation ax^2 + bx + c = 0 (a ≠ 0) are real and unequal and x lies between them.

What is the discriminant of 9×2 +2 10x?

We do this by subtracting 10x both sides (to get it on the other side).. 9x^2 + 2 = 10x 9x^2 – 10x + 2 = 10x – 10x 9x^2 – 10x + 2 = 0 Now the discriminant is: b^2 – 4ac The quadratic equation is Ax^2 + Bx + C = 0 Here, A = 9, B = -10 and C = 2 so plug them in…

What happens if the 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.

### How do you tell if a quadratic function is positive or negative?

Important Tidbit

1. A positive quadratic coefficient causes the ends of the parabola to point upward.
2. A negative quadratic coefficient causes the ends of the parabola to point downward.
3. The greater the quadratic coefficient, the narrower the parabola.
4. The lesser the quadratic coefficient, the wider the parabola.

### What is sign of expression?

When an expression is a product or a quotient, we can determine the sign of the expression on an interval by looking at the sign of each factor over the interval. For each expression, we determine the values of x (the independent variable) which make it positive, negative, zero, or undefined.

Do you include negative signs in quadratic formula?

This relationship is always true: If you get a negative value inside the square root, then there will be no real number solution, and therefore no x-intercepts. In other words, if the the discriminant (being the expression b2 – 4ac) has a value which is negative, then you won’t have any graphable zeroes.

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

The discriminant of is 76.

#### Which equation shows the quadratic formula used correctly?

Answer: Choice a is correct answer. we have to solve it by finding the value of x. ax²+bx+c = 0 is general quadratic equation.

#### How do you tell if a quadratic equation has no solution?

A quadratic equation has no solution when the discriminant is negative. From an algebra standpoint, this means b2 < 4ac. Visually, this means the graph of the quadratic (a parabola) will never touch the x axis. Of course, a quadratic that has no real solution will still have complex solutions.

When is the discriminant of the quadratic equation zero?

When a, b, and c are real numbers, a ≠ 0 and the discriminant is zero, then the roots α and β of the quadratic equation ax 2 + bx + c = 0 are real and equal. When a, b, and c are real numbers, a ≠ 0 and the discriminant is negative, then the roots α and β of the quadratic equation ax 2 + bx + c = 0 are unequal and not real.

Do you know the quadratic discriminant for roots?

From the above characterization of roots using the discriminant, we have the following: 1-4c > 0 , 1−4c > 0, then the polynomial has two distinct real roots. This occurs for . 1-4c = 0, 1−4c = 0, then the polynomial has a repeated root. This occurs for . 1 -4c < 0 , 1−4c < 0, then the roots are both non-real complex roots. This occurs for .

## When is the discriminant of the equation Ax 2 negative?

When a, b, and c are real numbers, a ≠ 0 and the discriminant is negative, then the roots α and β of the quadratic equation ax 2 + bx + c = 0 are unequal and not real. In this case, we say that the roots are imaginary.

## How to find the discriminant in problem 4?

Solution: Set the quadratic equation equal to 0 by adding 1 to both sides. Problem 4: Without calculating them, determine how many real solutions the equation 25 x2 – 40 x + 16 = 0 has. Set a = 3, b = -2, and c = 1, and evaluate the discriminant.