When a quadratic equation has positive roots?

When a, b, and c are real numbers, a ≠ 0 and the discriminant is positive, then the roots α and β of the quadratic equation ax2 +bx+ c = 0 are real and unequal. 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 ax2+ bx + c = 0 are real and equal.

Do all quadratic equations have at least one solution?

Yes. When the discriminant is zero, there are two unique solutions. When the discriminant is not zero, there is exactly one solution.

Which of the following quadratic equation does not have real roots?

Answer: A quadratic equation, ax2 + bx + c = 0; a ≠ 0 will have two distinct real roots if its discriminant, D = b2 – 4ac > 0. Hence, the equation x2 –3x + 4 = 0 has no real roots.

Why a quadratic equation Cannot have one real root and one complex root?

Because in formula for roots of quadratic equation decides the roots of quadratic equation to be complex or real. If is less than 0 then roots or complex or if is greater than 0 then roots are real. So both roots can be either be real or complex.

How do you know if a quadratic equation is positive?

However, when written in the form Ax^2+Bx+C=f(x), we can tell whether the parabola opens up or opens down by the sign of A. If A is positive, the parabola opens up. If A is negative, then it opens down.

Do all quadratic equations have a solution?

A quadratic equation has two solutions. Either two distinct real solutions, one double real solution or two imaginary solutions. All methods start with setting the equation equal to zero.

Does every quadratic equation have a solution?

Every quadratic equation has two solutions and can be factorized, but as level of difficulty rises, splitting may not be easy and one may tend to use quadratic formula.

What does it mean when a quadratic equation has only one solution?

A quadratic equation has one solution when the discriminant is zero. From an algebra standpoint, this means b2 = 4ac. Visually, this means the graph of the quadratic (a parabola) will have its vertex resting on the x-axis.

How do you know if a quadratic equation has no real roots?

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. – If b2 – 4ac < 0 then the quadratic function has no real roots.

How do you find a quadratic equation with all positive coefficients?

All the coefficients are positive, but there are no real roots. So a quadratic equation with all positive coefficients need not have positive real roots. If we have a quadratic with positive real roots a,b then f (x) = c (x-a)* (x-b) = c*x^2 -c* (a+b)*x + c*a*b.

How do you find a quadratic equation with positive real roots?

If we have a quadratic with positive real roots a,b then f (x) = c (x-a)* (x-b) = c*x^2 -c* (a+b)*x + c*a*b. So you can see that the linear coefficient has the opposite sign of the constant and quadratic terms. So a quadratic equation with all positive coefficients will never have positive real roots.

Why can’t a quadratic equation have a negative discriminant?

Since the quadratic formula requires taking the square root of the discriminant, a negative discriminant creates a problem because the square root of a negative number is not defined over the real line. An example of a quadratic function with no real roots is given by,

What is the discriminant of a quadratic function with two real roots?

If the discriminant of a quadratic function is greater than zero, that function has two real roots ( x -intercepts). Taking the square root of a positive real number is well defined, and the two roots are given by, f ( x) = 2 x2 − 11 x + 5. b2 − 4 ac = (−11) 2 − 4 · 2 · 5 = 121 − 40 = 81.