Can two quadratic equations have the same solution?

It’s clear that a system of two quadratic equations can have none, one or two solutions. For example: y=x2+2 and y=−x2+1 have none. y=x2, 2×2−8x+8 and y=−x2+8x−8 have 4 as common solution.

What does the discriminant of a quadratic equation tell you?

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.

How do you know if a quadratic equation is equal or unequal?

When a, b and c are real numbers, a ≠ 0 and discriminant is positive (i.e., b2 – 4ac > 0), then the roots α and β of the quadratic equation ax2 + bx + c = 0 are real and unequal.

What 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. Determine the nature of the solutions to each quadratic equation.

How many solutions can a quadratic equation have and why does it vary?

As we have seen, there can be 0, 1, or 2 solutions to a quadratic equation, depending on whether the expression inside the square root sign, (b2 – 4ac), is positive, negative, or zero. This expression has a special name: the discriminant.

Why does a quadratic equation have 2 solutions?

There are usually two solutions because quadratic equations form a parabola in Cartesian coordinates. In almost any case involving a function, the parabola will intercept the x-axis at two points. Those two points are the two x values that cause the function to be equal to zero.

What does value of discriminant mean?

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 no real roots.

What does the value of the discriminant mean?

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.

Why does a quadratic equation have two solutions?

How do you know if a quadratic equation has one solution?

The first way to tell if a quadratic has one solution is to look at the discriminant. If the discriminant is zero, then the quadratic equation has only one real solution. The discriminant is the expression b2 – 4ac under the radical in the quadratic formula.

What is the discriminant of the given equation?

What is the discriminant? The is the part of the quadratic formula under the square root. 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.

What does it mean when the discriminant of a quadratic equation is zero?

A discriminant of zero indicates that the quadratic has a repeated real number solution. A negative discriminant indicates that neither of the solutions are real numbers.

What is the difference between linear and quadratic discriminant function?

Quadratic discriminant function: This quadratic discriminant function is very much like the linear discriminant function except that because Σ k, the covariance matrix, is not identical, you cannot throw away the quadratic terms. This discriminant function is a quadratic function and will contain second order terms.

What does a positive discriminant mean in math?

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.