Which of the following quadratic equation has no real roots?

Solution: A quadratic equation ax² + bx + c = 0 has no real roots if discriminant < 0. Hence option A is the answer.

Which quadratic equation has no real roots?

A quadratic equation ax² + bx + c = 0 has no real roots when the discriminant of the equation is less than zero. Therefore, the equation has no real roots.

Which of the quadratic equation has real roots?

A quadratic equation has real roots when the discriminant is positive or zero (not negative). From an algebra standpoint, this means b² >= 4ac. Visually, this means the graph of the quadratic (a parabola) touches the x axis at least once.

Which of the following has no real roots x2 4x 3 √ 2?

• x² + 4x + 3√2 = 0

So that , OPTION (b) & OPTION (d) have no real roots.

Can a quadratic equation ax2 bx 0 has non real roots?

No because , Here the value of c = 0.

Condition For No Real Roots Test

For what value S of a quadratic equation 30ax2 6x 1 0 has no real roots?

Answer: For values of 'a' greater than 3/10, given quadratic equation will have no real roots.

Is 0 A real root?

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, there is exactly one real root. This value of x is the one distinct real root of the given equation.

What is are the real roots of the equation?

The real roots are expressed as real numbers. Suppose ax² + bx + c = 0 is a quadratic equation and D = b2 – 4ac is the discriminant of the equation such that: If D = 0, then the roots of the equation are real and equal numbers.

How do you find real roots?

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 one repeated real root.

For what value of k equation has no real roots?

To have no real roots means discriminant should be less than zero. Therefore, for k<-9 the quadratic equation will have no real roots.

How many real roots does the quadratic equation?

The number of roots of a polynomial equation is equal to its degree. So, a quadratic equation has two roots.

Which of the following is not a quadratic equation?

option B is a linear equation, not a quadratic equation.

What are real and non real roots?

If Δ<0, then roots are imaginary (non-real) and beyond the scope of this book. If Δ≥0, the expression under the square root is non-negative and therefore roots are real. For real roots, we have the following further possibilities. If Δ=0, the roots are equal and we can say that there is only one root.

How many real roots are there?

When you solve for the roots of a quadratic equation, there are several possible outcomes. You can have two real number solutions. If you set x equal to either solution, the result with be zero both times. There can be just one real number solution.

What's a real root?

Given an equation in a single variable, a root is a value that can be substituted for the variable in order that the equation holds. In other words it is a "solution" of the equation. It is called a real root if it is also a real number. For example: x2−2=0.

What are real roots Class 10?

A real number x is called a root of the quadratic equation ax² + bx + c =0, a 0 if aα² + bα + c =0.In this case, we say x = α is a solution of the quadratic equation.

Which quadratic equation has roots that are real numbers and equal?

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.

Can zero be a root of a quadratic equation yes or no?

Answer: Roots are also called x-intercepts or zeros. A quadratic function is graphically represented by a parabola with vertex located at the origin, below the x-axis, or above the x-axis. Therefore, a quadratic function may have one, two, or zero roots.

Is 0 a real solution in quadratic equation?

A quadratic equation does not always have a real solution. However, a quadratic equation always has a solution if we consider complex/imaginary numbers. In terms of real solutions, there are always either 0, 1, or 2 real solutions to a quadratic equation, depending on the sign of the discriminant.

Is 0 a quadratic equation?

In this case there is a distinct break at a=0 in both the theoretical and practical world. At a=0 in the theoretical world the equation is no longer a quadratic, so in the practical world one must test in some way for that.

For what value of a the quadratic equation 3ax 2 6x 1 0 has real and equal roots?

If D = 0 , then the roots are real and equal . If D > 0 , then the roots are real and distinct .

For what value is the quadratic equation 9x2 3ax 1 0?

Expert-verified answer

A=9,B=−3a,C=1.

Why does a quadratic equation have to be in standard form before applying the quadratic formula to find solutions?

The form ax² + bx + c = 0 is called standard form of a quadratic equation. Before solving a quadratic equation using the Quadratic Formula, it's vital that you be sure the equation is in this form. If you don't, you might use the wrong values for a, b, or c, and then the formula will give incorrect solutions.

How do you find no real roots?