Table of Contents

## How many solutions does x 2 5x 7 have?

Using the quadratic formula, you can find out that the quadratic has **two real solutions.**

## How many real roots does x 2 5x 7?

1 real root

## What will be the nature of roots of quadratic equation 2x 2 − 5x − 7 0?

the roots **are real and equal.**

## What is the nature of the roots of the equation x2 5x 7 0?

The nature of roots of quadratic equation x2-5x-70 are **real and equal.**

## How do you know how many solutions a quadratic equation has?

**The discriminant can be positive, zero, or negative, and this determines how many solutions there are to the given quadratic equation.**

- A positive discriminant indicates that the quadratic has two distinct real number solutions.
- A discriminant of zero indicates that the quadratic has a repeated real number solution.

## Can X have two solutions?

There are **usually two solutions because quadratic equations form a parabola in Cartesian coordinates. In almost any case involving a function, the parabola will intercept the x-axis at two points. Those two points are the two x values that cause the function to be equal to zero.**

## What is the sum of the roots of 2x 2 5x =- 7?

Cliff solved the equation 2x^2 – 5x + 7 0 and noticed that the sum of the roots was **5/2 and the product of the roots was 7/2.**

## How many solutions does x 2 have?

X^2n in the set of real numbers it has **infinitely many solutions for assuming n positive or zero xsqrt(n) and for a positive or zero n the function xsqrt(n) is unbounded. So the range is [0,infinity[ which means infinite number of solutions.**

## How many real roots does this equation have?

two real roots

## What is the nature of roots of the equation x 2 5x 7 0?

The nature of roots of quadratic equation x2-5x-70 are **real and equal.**

## How many real roots does a quadratic equation 2 5 7 0 have?

Therefore there are **2 roots.**

## What will be the nature of the roots of quadratic equation 2x 2 4x 7 0?

The nature of roots of quadratic equation x2-5x-70 are **real and equal.**

## What is the nature of the roots of the quadratic equation 3x 2 5x 2 0?

Hence, roots of the quadratic equation are **real and unequal.**

## What will be the nature of roots of quadratic equation?

If D is equal to 0, then we get **two roots which are equal and same. If D is less than 0, then we get roots which are imaginary or unreal. Since D is greater than 0 in this case, we get two real and distinct roots. Hence solved !!**

## How do you find the nature of the roots of the equation?

To determine the nature of roots of quadratic equations (in the form ax^2 + bx +c0) , 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 the roots of the quadratic equation x² 5x 36 0?

the roots **are real and equal.**

## How many solution does the quadratic equation x2 5x 7 0?

Answer: **Roots are real and distinct.**

## How do you know how many solutions a quadratic has?

**The discriminant can be positive, zero, or negative, and this determines how many solutions there are to the given quadratic equation.**

- A positive discriminant indicates that the quadratic has two distinct real number solutions.
- A discriminant of zero indicates that the quadratic has a repeated real number solution.

## How do you determine the solutions of quadratic equations?

How To Solve Them? The solutions to the Quadratic Equation are where it is equal to zero. There are usually 2 solutions (as shown in this graph). Just **plug in the values of a, b and c, and do the calculations.**

## How do you know how many solutions an equation has?

If solving an equation yields a statement that is true for a single value for the variable, like x 3, then the equation has one solution. If solving an equation yields a statement that is always true, like 3 3, then the equation has **infinitely many solutions**

## How do you know if a quadratic equation has one solution?

The first way to tell if a quadratic has one solution is **to look at the discriminant. If the discriminant is zero, then the quadratic equation has only one real solution. The discriminant is the expression b**2 4ac under the radical in the quadratic formula.

## Can an equation have two solutions?

**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 X 2 have two solutions?

In general, all equations of the form x2 a, where a is a positive number, will always give two solutions, namely **x – / a or x / a.**

## How do you know if an equation has two solutions?

Here’s how the discriminant works. Given a quadratic equation ax2 + bx + c 0, plug the coefficients into the expression b2 – 4ac to see what results: **If you get a positive number, the quadratic will have two unique solutions. If you get 0, the quadratic will have exactly one solution, a double root.**

## How do you find the sum of the roots?

**For a quadratic equation ax2 + bx + c 0,**

- The roots are calculated using the formula, x (-b xb1 u221a (bxb2 – 4ac) )/2a.
- Discriminant is, D b2 – 4ac. If D x26gt; 0, then the equation has two real and distinct roots. If D x26lt; 0, the equation has two complex roots.
- Sum of the roots -b/a.
- Product of the roots c/a.