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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.
## What is the shortcut to find the roots of a quadratic equation?

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

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## Which of the following is fastest method to find the roots of equation?

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

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

## Quadratic Equation – Finding Roots Shortcut Example 4

## How To Solve Quadratic Equations By Factoring – Quick & Simple!

- 1) a+b+c=0 then the roots are 1 and c/a. Example: 33×2−41x+8=0 has 1 and 8/33 as solutions.
- 2) b=a+c then the roots are −1 and −c/a. Example: 1793×2+2016x+223 has −1 and −223/1793 as roots.
- 3) for x2+bx+c=0 I test the divisors of c. If one of them say α is a root then c/α is a root.

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.

The fastest root-finding method we have included is **Newton’s method**, which uses the derivative at a point on the curve to calculate the next point on the way to the root. Accuracy with this method increases as the square of the number of iterations.

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.

You just **need to divide the constant term of the quadratic by the known root**. Example: If one root of the quadratic equation is given as 5, then the other root is . 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.

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 $\alpha \beta =\dfrac{c}{a}$.

– 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. 1 The **equation x2 + 3pq + p = 0**, where is a non-zero constant, has equal roots.

I currently know **three** main methods of finding roots: the Secant method, the Newton-Raphson method and the Interval Bisection method.

To use the quadratic formula to find the roots of a quadratic equation, all we have to do is get **our quadratic equation into the form ax2 + bx + c = 0; identify a, b, and c**; and then plug them in to the formula.

Root-finding problem is of the **most basic problems of numerical approximation**. This process involves finding a root (or zero, or solution), of an equation of the form f (x) = 0, for a given function f . Often it will not be possible to solve such root-finding problems analytically.

Steps to factorize quadratic equation ax^{2} + bx + c = 0 using completeing the squares method are: Step 1: Divide both the sides of quadratic equation ax^{2} + bx + c = 0 by a. Now, the obtained equation is **x ^{2} + (b/a) x + c/a = 0**. Step 2: Subtract c/a from both the sides of quadratic equation x

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.

Hint: A quadratic equation has equal roots iff its discriminant is zero. A quadratic equation has equal roots **iff these roots are both equal to the root of the derivative**.

**When discriminant is greater than zero**, the roots are unequal and real. When discriminant is equal to zero, the roots are equal and real. When discriminant is less than zero, the roots are imaginary.

on the value of the root may produce a value of the polynomial at the approximate root that is of the order of. For avoiding these problems, methods have been elaborated, which compute all roots simultaneously, to any desired accuracy. Presently the most efficient method is **Aberth method**.

We should clarify that the purpose of **the bisection method**, as with any other iteration method for finding real roots, is not to get the exact root. Rather, it is to find a “sufficiently small” interval that definitely contains the root.

A trick that lets you get closer and closer to an exact answer is a “numerical method”. … So that there is the answer: we need numerical methods **because a lot of problems are not analytically solvable and we know they work because each separate method comes packaged with a proof that it works**.

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.

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