When b2 4ac is greater than zero but not a perfect square then the roots are?

Case V: b2 – 4ac > 0 and not perfect square When a, b and c are real numbers, a ≠ 0 and discriminant is positive but not a perfect square then the roots of the quadratic equation ax2 + bx + c = 0 are real, irrational and unequal. Here the roots α and β form a pair of irrational conjugates.

What does it mean if the discriminant is greater than 0?

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 the discriminant is greater than zero but not 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.

What does it implies when the value of b2 4ac is zero?

A negative under the radical means there are no real number solutions to the radical. b2−4ac<0: The equation has 0 real solutions. The graph does not cross the x-axis. b2−4ac=0: The equation has 1 real solution.

What does it mean 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.

How many solution’s are there if the value of the discriminant is less than 0?

one solution
It tells you the number of solutions to a quadratic equation. 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.

What are the roots of the equation ax2 bx c 0?

The roots of a function are the x-intercepts. By definition, the y-coordinate of points lying on the x-axis is zero. Therefore, to find the roots of a quadratic function, we set f (x) = 0, and solve the equation, ax2 + bx + c = 0.

What is the roots of ax2 bx c 0?

In a quadratic equation ax2 + bx + c = 0, a ≠ 0 the coefficients a, b and c are real. We know, the roots (solution) of the equation ax2 + bx + c = 0 are given by x = −b±√b2−4ac2a. 1. If b2 – 4ac = 0 then the roots will be x = −b±02a = −b−02a, −b+02a = −b2a, −b2a.

What is the value of B²-4ac?

b²-4ac = 0. The roots are equal. The curve just touches the x axis at 1 point. b²-4ac > 0. You can take the + or – square root so there are 2 real roots. Rep:? You get these gems as you gain rep from other members for making good contributions and giving helpful advice. Are you familiar with the quadratic formula?

How do you find the square root of B²-4ac?

If b²-4ac=0, then x=-b/2a, i.e. one root. If b²-4ac>0, then x=(-b ± k)/2a, i.e. two roots. If b²-4ac<0, you’d take the square root of a negative number, so no real roots exist.

When are the roots of a quadratic equation irrational and unequal?

When a, b, and c are real numbers, a ≠ 0 and the discriminant is positive but not a perfect square then the roots of the quadratic equation ax 2 + bx + c = 0 are real, irrational and unequal. Here the roots α and β form a pair of irrational conjugates. Case VI: b 2 – 4ac > 0 is perfect square and a or b is irrational

Are the roots of ax2 + bx + c = 0 equal?

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