What if a quadratic equation has only one root?

2 Answers By Expert Tutors 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.

Does a quadratic equation always have two roots?

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. are given by the quadratic formula.

How do you know if an equation has two roots?

To work out the number of roots a qudratic ax2​+bx+c=0 you need to compute the discriminant (b2​-4ac). If the discrimant is less than 0, then the quadratic has no real roots. If the discriminant is equal to zero then the quadratic has equal roosts. If the discriminant is more than zero then it has 2 distinct roots.

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.

What is the two roots of a quadratic equation?

The roots of the quadratic equation ax2 + bx + c = 0 are nothing but the solutions of the quadratic equation. i.e., they are the values of the variable (x) which satisfies the equation. The roots of a quadratic function are the x-coordinates of the x-intercepts of the function.

How many roots can a quadratic equation have?

two
A quadratic equation with real coefficients can have either one or two distinct real roots, or two distinct complex roots. In this case the discriminant determines the number and nature of the roots.

How do I find the root of one root?

Now, we can find the other root by the formula for sum and product of the roots. If $\alpha$ and $\beta$ are the two roots of the quadratic equation $a{{x}^{2}}+bx+c=0$ then the sum and product of the roots are given by the formula: $\alpha +\beta =\dfrac{-b}{a}$ and $\alpha \beta =\dfrac{c}{a}$.

What are the two roots of quadratic equation?

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.

How many roots are in a quadratic equation?

A quadratic equation with real or complex coefficients has two solutions, called roots.

How to find the other root of a quadratic equation?

If the root given is rational, then we can use the product of the roots rule. The product of the roots of the quadratic equation a x 2 + b x + c = 0 is c a. So, in this case, we can find the other root by dividing this product by the given root. If the co-efficient of x 2 is ‘1’ ( i. e. a = 1 ), then this becomes much easier.

How do you find the other root of x^2?

The product of the roots of the quadratic equation a x 2 + b x + c = 0 is c a. So, in this case, we can find the other root by dividing this product by the given root. If the co-efficient of x 2 is ‘1’ ( i. e. a = 1 ), then this becomes much easier. You just need to divide the constant term of the quadratic by the known root.

How do you find the zeros of a quadratic equation?

This quadratic equation root calculator lets you find the roots or zeroes of a quadratic equation. A quadratic is a second degree polynomial of the form: ax^2+bx+c=0 where a\ eq 0.To solve an equation using the online calculator, simply enter the math problem in the text area provided.

What are the maximum and minimum values of a quadratic equation?

Also, the maximum and minimum values of a quadratic equation f(x) occurs at x = -b/2a. If the given quadratic equation is in the form f(x) = a(x – h) 2 + m, Then the value of ‘m’ (vertex) gives us the minimum (when ‘a’ is negative) or maximum (when ‘a’ is positive) values of the given function.