How do you find the roots of a second-degree equation?

The roots of any quadratic equation is given by: x = [-b +/- sqrt(-b^2 – 4ac)]/2a. Write down the quadratic in the form of ax^2 + bx + c = 0. If the equation is in the form y = ax^2 + bx +c, simply replace the y with 0. This is done because the roots of the equation are the values where the y axis is equal to 0.

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 is the formula for finding 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 x2. The quadratic equation having roots α, β, is x2 – (α + β)x + αβ = 0.

Which of the following is a second degree equation?

quadratic equation
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.

How do we find the sum and product of the roots without finding the actual roots?

But the sum and the product of roots of a quadratic equation ax2 + bx + c = 0 can be found without actually calculating the roots. Let us see how. We know that the roots of the quadratic equation ax2 + bx + c = 0 by quadratic formula are (-b + √ (b² – 4ac) )/2a and (-b – √ (b² – 4ac) )/2a.

How do you show that the roots of an equation are real?

The discriminant (EMBFQ)

1. If Δ<0, then roots are imaginary (non-real) and beyond the scope of this book.
2. If Δ≥0, the expression under the square root is non-negative and therefore roots are real.
3. If Δ=0, the roots are equal and we can say that there is only one root.

How to find the equation with one root 2 + 3i?

If an equation has one root 2 + 3i, then it will also have a root at the conjugate of 2 + 3i, which is 2 – 3i. So you will have the equation . This is like solving a quadratic equation by completing the square, with the steps in reverse:

How do you factor 2 + 3i into a quadratic equation?

Then we can write the factorised version: (x-2-3i)* (x-2-3i)=0. Multiply this out fully and remember that and you will get your quadratic. You can put this solution on YOUR website! If an equation has one root 2 + 3i, then it will also have a root at the conjugate of 2 + 3i, which is 2 – 3i.

How do you find the root of a polynomial?

Root is nothing but the value of the variable that we find in the equation.To get a equation from its roots, first we have to convert the roots as factors. By multiplying those factors we will get the required polynomial. 2 and 3 are the roots of the polynomial then we have to write it as x = 2 and x = 3.

How to find the polynomial with 2 and 3 factors?

By multiplying those factors we will get the required polynomial. 2 and 3 are the roots of the polynomial then we have to write them as The product of those factors will give the polynomial. Because we have two factors, we will get a quadratic polynomial. Roots and zeroes are same.