Can the root of a quadratic equation be zero?

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.

What if a quadratic equation has only one root?

2 Answers By Expert Tutors. You can write these equations in vertex form. If the vertex of the equation has a y-coordinate of 0, then the equation has only one root. If the value of k is zero, then the equation has one root.

What are the conditions for roots of quadratic equation?

To determine the nature of roots of quadratic equations (in the form ax^2 + bx +c=0) , we need to caclulate the discriminant, which is b^2 – 4 a c. When discriminant is greater than zero, the roots are unequal and real. When discriminant is equal to zero, the roots are equal and real.

What is the nature of roots of a quadratic equation of 0?

Clearly, the discriminant of the given quadratic equation is zero. Therefore, the roots are real and equal.

Is 0 a solution to a quadratic equation?

If there is no constant term (that is, x itself is a factor of the quadratic), then yes, 0 is actually a solution.

What is the condition for one root of the quadratic equation ax2 bx c 0 to be twice the other?

ax2 + bx + c = 0. ⇒ 2b2 = 9ac. Hence Proved.

How do you write a quadratic equation with one zero?

In general form we can find as many quadratic polynomials as we want by replacing 2 by k where k is any value like, 1, 2, 3, … etc. All quadratic polynomials with any value of k have only one zero. So, a quadratic polynomial that has only one zero is (x−2)2 .

How do you write a quadratic equation with zeros?

Let the polynomial be ax2 + bx + c and its zeros be α and β. If k = 4, then the polynomial is 4×2 – x – 4. Example 6: Find a cubic polynomial with the sum of its zeroes, sum of the products of its zeroes taken two at a time, and product of its zeroes as 2, – 7 and –14, respectively.

What equations have no real roots?

If the discriminant is greater than zero, this means that the quadratic equation has no real roots. Therefore, there are no real roots to the quadratic equation 3×2 + 2x + 1. If the discriminant is equal to zero, this means that the quadratic equation has two real, identical roots.

Which of the following quadratic equations have no 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.

How to find the other root of a quadratic equation?

(ii) We can find the other root or roots by using the relations between roots and coefficients of the given equations Let α, β be the common roots of the quadratic equations a 1 x 2 + b 1 x + c 1 = 0 and a 2 x 2 + b 2 x + c 2 = 0.

What are the zeros of a quadratic equation called?

These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation. The polynomial equation whose highest degree is two is called a quadratic equation or sometimes just quadratics.

What is the meaning of quadratic equation?

1 Quadratic Equation Definition. The polynomial equation whose highest degree is two is called a quadratic equation or sometimes just quadratics. 2 Quadratics Formula. The formula for a quadratic equation is used to find the roots of the equation. 3 Examples of Quadratics. 4 Video Lesson.

How do you find the common root of two equations?

The common root is given by α = c 1 a 2 – c 2 a 1 /a 1 b 2 – a 2 b 1 or, α = b 1 c 2 – b 2 c 1 /c 1 a 2 – c 2 a 1 (i) We can find the common root by making the same coefficient of x 2 of the given equations and then be subtracting the two equations.