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For a quadratic equation ax^{2} + bx + c = 0, The roots are calculated using the formula, **x = (-b ± √ (b² – 4ac) )/2a**. Discriminant is, D = b^{2} – 4ac. If D > 0, then the equation has two real and distinct roots.

The formula to find the roots of the quadratic equation is **x = −b±√b2−4ac2a − b ± b 2 − 4 a c 2 a** . The sum of the roots of a quadratic equation is α + β = -b/a = – Coefficient of x/ Coefficient of x^{2}. The quadratic equation having roots α, β, is x^{2} – (α + β)x + αβ = 0.
## How do you find roots of a function?

## How do you find the number of roots in a quadratic function?

## How do you find the roots of a quadratic graph?

To work out the number of roots a qudratic ax^{2}+bx+c=0 you need **to compute the discriminant (b ^{2}-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.

The roots of a quadratic equation are **the 𝑥-coordinates of the points on the graph that have 𝑦-coordinates of zero**, so the 𝑥-values in the equation that generate a 𝑦-value of zero — in other words the points where it cuts the 𝑥-axis.
## How do you find the roots of a quadratic equation in Class 10?

## How do you find roots without solving?

## How do you find the roots zeros from a quadratic equation?

## Is a root of a quadratic equation?

Roots of a Quadratic equation

The values of x for which a quadratic equation is satisfied are called the roots of the quadratic equation. If α is a root of the quadratic equation ax2+bx+c=0, then a**α2+bα+c=**0.

Roots of Quadratic Equation. The values of variables satisfying the given quadratic equation are called its roots. In other words, **x = α is** a root of the quadratic equation f(x), if f(α) = 0. The real roots of an equation f(x) = 0 are the x-coordinates of the points where the curve y = f(x) intersect the x-axis.
## How do you find the roots of a quadratic function in Python?

**Example –**
## What is the quadratic equation if the roots are 2 and 6?

## How do you identify the roots?

## How do you find the real roots of an equation?

## How do you find the sum and product of the roots of a quadratic equation?

## What is the sum of the roots of a quadratic equation?

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## What are the nature of roots of quadratic equation?

## What is the basic quadratic equation?

## What are roots of the quadratic equation x2 49 0?

## What is the root of 5x 8 7?

## What are the roots of the quadratic equation x2 5x =- 6?

## What completely determines the types of roots of a quadratic function?

## When can be the roots of quadratic equation has real roots?

## How do you know if a quadratic equation has real roots?

## How many real roots does the quadratic equation?

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## Can you solve the quadratic equation given its roots?

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## What are roots of the quadratic equation 2x² 6?

## How to find the roots of an quadratic equation – Free Math Help

## Find the roots of a quadratic using the quadratic formula

## Rewriting a quadratic function to find roots and vertex | Algebra I | Khan Academy

## Quadratic Equation – Finding Roots Shortcut Example 4

- # Python program to find roots of quadratic equation.
- import math.
- # function for finding roots.
- def findRoots(a, b, c):
- dis_form = b * b – 4 * a * c.
- sqrt_val = math.sqrt(abs(dis_form))
- if dis_form > 0:
- print(” real and different roots “)

**x2+8x+12=0** is a quadratic equation with roots -2 and -6. Note: We know that if a and b are the roots of a quadratic equation, then one such equation is given by x2−(a+b)x+ab=0. Hence the quadratic equation with roots -2 and -6 is x2+8x+12=0.

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.

You can find the roots, or solutions, of the polynomial equation P**(x) = 0 by setting each factor equal to 0 and solving for x**. Solve the polynomial equation by factoring. Set each factor equal to 0. 2×4 = 0 or (x – 6) = 0 or (x + 1) = 0 Solve for x.

For a quadratic equation ax^{2}+bx+c = 0, the sum of its roots **= –b/a** and the product of its roots = c/a. A quadratic equation may be expressed as a product of two binomials.

**x2+4x=0**.

First factorize the polynomial. Equate each factor to zero. The roots of the equation are **x = 1, 10 and 12**. Solve the cubic equation x^{3} – 6 x^{2} + 11x – 6 = 0.

We can see, the discriminant of the given quadratic equation is positive but not a perfect square. Hence, the roots of a quadratic equation are **real, unequal and irrational**.

A quadratic equation is an equation of the second degree, meaning it contains at least one term that is squared. The standard form is **ax² + bx + c = 0** with a, b and c being constants, or numerical coefficients, and x being an unknown variable.

By the three methods also we obtain the same solution. Hence, after solving the given quadratic equation $ {x^2} – 49 = 0 $ we get the roots of x=7 or **x=-7**. So, the correct answer is “ $ x = 7 $ OR $ x = – 7 $ ”.

7=7. so, **x=3** is your answer.

Answer: Using the quadratic formula, the roots of the equation x^{2} – 5x + 6 are **2 and 3**.

In order to determine these type of roots, we can look at **the discriminant, which is 𝑏 squared minus four 𝑎𝑐**. If it ends up being less than zero, it will have two different complex and nonreal roots. If 𝑏 squared minus four 𝑎𝑐 ends up being equal to zero, it will have two real and equal roots.

A quadratic equation has real roots **when the discriminant is positive or zero (not negative)**. From an algebra standpoint, this means b^{2} >= 4ac.

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**. – If b2 – 4ac < 0 then the quadratic function has no real roots.

two

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

How Many Roots? **Examine the highest-degree term of the polynomial** – that is, the term with the highest exponent. That exponent is how many roots the polynomial will have. So if the highest exponent in your polynomial is 2, it’ll have two roots; if the highest exponent is 3, it’ll have three roots; and so on.

When we solve quadratic equations we get solutions called roots or places where that function crosses the x axis. … If you were given only two x values of the roots then put them into the form that would give you those two x values (when set equal to zero) and multiply to see if you get the original function.

Therefore, the roots (solution) are real and unequal. Note: Let a, b and c be rational numbers in the equation ax2 + bx + c = 0 and its discriminant b2 – 4ac > 0.

…

Examine the Roots of a Quadratic Equation.

…

Examine the Roots of a Quadratic Equation.

Discriminant of ax2 + bx + c = 0 | Nature of roots of ax2 + bx + c = 0 | Value of the roots of ax2 + bx + c = 0 |
---|---|---|

b2 – 4ac > 0 | Real and unequal | −b±√b2−4ac2a |

Hence, **2 and -3/2** are the roots of the given equation.

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