Can a quadratic equation have two positive answers?

You can have a quadratic with vertex in the positive numbers, but one root positive and one root negative. For example, take (x+1)(x−4)=x2−3x−4. The minimum occurs at x=32, but one root is negative. So while having the vertex in the positive numbers is necessary, it is not sufficient.

What happens when the a value in quadratic equations is positive?

If A is positive, the parabola opens up. If A is negative, then it opens down. If we want to determine for what values of x the function will be positive (or negative), we need to solve Ax^2+Bx+C=0 (that is, where does the function cross the x-axis?).

What is the positive solution to the 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. A negative discriminant indicates that neither of the solutions are real numbers.

How do you prove that a quadratic is always positive?

You can prove it by another method. x²−2x+5 is always positive and it can be proved in many ways. As the discriminant is negative, the quadratic equation has no real root. And if we put x=0, then the equation will be 5 which is positive so the equation totally lies above the real axis.

What is positive solution of an equation?

1, a positive solution of this equation may be obtained by assigning to each unknown in the left member of the equation a value equal to the sum of all the coefficients in the right member, and to each unknown in the right member a value equal to the sum of all the coefficients in the left member.

How do you solve a quadratic equation with two solutions?

It is called the Discriminant, because it can “discriminate” between the possible types of answer:

1. when b2 − 4ac is positive, we get two Real solutions.
2. when it is zero we get just ONE real solution (both answers are the same)
3. when it is negative we get a pair of Complex solutions.

Can a quadratic equation be both negative and positive?

In general, not all quadratics will be entirely positive or entirely negative but you can always convert ax2 + bx + c = a(x2 + b / ax + b2 / 4a2) + c − b2 / a = a(x + b / 2a)2 + (c − b2 / a) The term squared will always be non-negative. If a and (c – b^2/a) are both positive or are both negative the quadratic will be…

How do you find the root of a quadratic equation?

The roots could be positive or negative, real or imaginary. You factor the quadratic equation snd then you can detetmine if each root will be positive or negative. Factor it. In this case, find two numbers that when added together = 5 (the middle term) and when multiplied together = 6 (the final term). Either -5 or -6 will make the equation = 0.

How do you find the standard form of a quadratic equation?

A quadratic equation in its standard form is represented as: \\(ax^2 + bx + c\\) = \\(0\\), where \\(a,~b ~and~ c\\) are real numbers such that \\(a ≠ 0\\) and \\(x\\) is a variable. The number of roots of a polynomial equation is equal to its degree.

What does it mean if the root of an equation is negative?

D < 0: When D is negative, the equation will have no real roots. This means the graph of the equation will not intersect x-axis. Let us take some examples for better understanding. Since D>0, the equation will have two real and distinct roots.