Question

How to find the roots of a quadratic equation with leading coefficient greater than 1?

Answer 1

To find the roots of a quadratic equation with any leading coefficient, the quadratic formula x = (-b ± √(b² - 4ac)) / (2a) is used. The discriminant, b² - 4ac, indicates the nature of the roots. The process is the same regardless of whether the leading coefficient is 1 or greater.

Step-by-step explanation:

To find the roots of a quadratic equation with a leading coefficient greater than 1, you can use the quadratic formula. The standard form of a quadratic equation is ax² + bx + c = 0. When a is not equal to one, the equation is still solved in the same way as when a is one.
To use the quadratic formula, you will apply the following steps:

1. Identify the coefficients a, b, and c in the equation.
2. Plug these values into the quadratic formula, which is: x = (-b ± √(b² - 4ac)) / (2a).
3. Calculate the discriminant, which is the part under the square root sign, b² - 4ac. This will determine the nature of the roots (whether they are real or complex).
4. Calculate the two possible values for x by using the plus and minus signs in the quadratic formula.
5. If the discriminant is positive, there are two real and distinct roots. If it is zero, there is one real root (a repeated root). If the discriminant is negative, the roots are complex and involve the imaginary unit i.

Even with a leading coefficient greater than 1, the process is the same. If necessary, you can perform such operations with a calculator capable of computing square roots and other calculations as required. Some problems may simplify further if the equation is a perfect square or can be factorized easily.

Answer 2

A quadratic equation in its generic form can be written as:
ax ^ 2 + bx + c = 0
For this case:
a> 1
For this case what you should do is use the following equation
roots = ((- b) +/- root (b ^ 2-4 * a * c)) / (2 * a)
answer
root1 = ((- b) + root (b ^ 2-4 * a * c)) / (2 * a)
root2 = ((- b) - root (b ^ 2-4 * a * c)) / (2 * a)