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A quadratic equation has the form:
x^2 - (sum of the roots)x + (product of the roots) = 0
If the roots are imaginary roots, these roots are complex number a+bi and its conjugate a - bi, where a is the real part and b is the imaginary part of the complex number.
Their sum is:
a + bi + a - bi = 2a
Their product is:
(a + bi)(a - bi) = a^2 + b^2
Thus the equation will be in the form:
x^2 - 2a(x) + a^2 + b^2 = 0 or,
x^2 - 2(real part)x + [(real part)^2 + (imaginary part)^2]= 0
For example if the roots are 3 + 5i and 3 - 5i, the equation will be:
x^2 - 2(3)x + 3^2 + 5^2 = 0
x^2 - 6x + 34 = 0 where,
a = 1, b = -6, and c = 34.
Look at the denominator of this quadratic equation:
D = b^2 - 4ac.
D = (-6)^2 - (4)(1)(34) = 36 - 136 = -100
D < 0
Since D < 0 this equation has two imaginary roots.
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What is the graph of a quadratic formula?
In general, quadratic equations have graphs that are parabolas. The quadratic formula tells us how to find the roots of a quadratic equations. If those roots are real, they are the x intercepts of the parabola.
What is the difference between quadratic function and quadratic formula?
A quadratic function is a function where a variable is raised to the second degree (2). Examples would be x2, or for more complexity, 2x2+4x+16. The quadratic formula is a way of finding the roots of a quadratic function, or where the parabola crosses the x-axis. There are many ways of finding roots, but the quadratic formula will always work for any quadratic function. In the form ax2+bx+c, the Quadratic Formula looks like this: x=-b±√b2-4ac _________ 2a The plus-minus means that there can 2 solutions.
What are the pros and cons of solving quadratics by using the quadratic formula?
One pro of using the quadratic formula is that it will produce complex (imaginary) roots just as easily as it can produce real roots. (Factoring with imaginary numbers is a kind of a nightmare!) Another pro to the quadratic formula is that it eliminates the frustrating guess-and-check process. A con of the quadratic formula is that, when it comes to more simple problems, it is usually more time-consuming. A lot of textbook problems are quite easy to factor in your head--it is often not worth the effort of plugging numbers into a long formula. A second con of the quadratic formula is that it is quite long--you might write out the formula, accidentally forget a letter, and whole thing is useless. It's much easier to see that your work is correct when you're factoring.
What is the quadratic formula used for?
The quadratic formula is used all the time to solve quadratic equations, often when the factors are fractions or decimals but sometimes as the first choice of solving method. The quadratic formula is sometimes faster than completing the square or any other factoring methods. Quadratic formula find: -x-intercept -where the parabola cross the x-axis -roots -solutions
What are the roots of the quadratic equation below?
That depends on the equation.
When do you use the quadratic formula?
When you need to find the roots of a quadratic equation and factorisation does not work (or you cannot find the factors). The quadratic equation ALWAYS works. And when appropriate, it will give the imaginary roots which, judging by this question, you may not yet be ready for.
What is the graph of a quadratic formula?
In general, quadratic equations have graphs that are parabolas. The quadratic formula tells us how to find the roots of a quadratic equations. If those roots are real, they are the x intercepts of the parabola.
What is a parabola and quadratic?
A parabola is a line with one curve, that usually crosses the x-axis of a graph twice (unless the roots are imaginary). To find the roots, set y to zero and use the quadratic formula (-b±√b^2-4AC/2A)
Can the answer to a quadratic equation be a decimal?
Yes. You can calculate the two roots of a quadratic equation by using the quadratic formula, and because there are square roots on the quadratic formula, and if the radicand is not a perfect square, so the answer to that equation has decimal.
The discriminant determines how many what a quadratic equation will have whether they are real or imaginary?
roots
Why do you use square roots to solve quadratic equations?
Because it's part of the quadratic equation formula in finding the roots of a quadratic equation.
Why do mathmaticians use the quadratic formula?
To find the roots (solutions) of a quadratic equation.
What is the difference between quadratic function and quadratic formula?
A quadratic function is a function where a variable is raised to the second degree (2). Examples would be x2, or for more complexity, 2x2+4x+16. The quadratic formula is a way of finding the roots of a quadratic function, or where the parabola crosses the x-axis. There are many ways of finding roots, but the quadratic formula will always work for any quadratic function. In the form ax2+bx+c, the Quadratic Formula looks like this: x=-b±√b2-4ac _________ 2a The plus-minus means that there can 2 solutions.
What are the pros and cons of solving quadratics by using the quadratic formula?
One pro of using the quadratic formula is that it will produce complex (imaginary) roots just as easily as it can produce real roots. (Factoring with imaginary numbers is a kind of a nightmare!) Another pro to the quadratic formula is that it eliminates the frustrating guess-and-check process. A con of the quadratic formula is that, when it comes to more simple problems, it is usually more time-consuming. A lot of textbook problems are quite easy to factor in your head--it is often not worth the effort of plugging numbers into a long formula. A second con of the quadratic formula is that it is quite long--you might write out the formula, accidentally forget a letter, and whole thing is useless. It's much easier to see that your work is correct when you're factoring.
What is the formula to find the product of the roots of a quadratic equation?
If the quadratic is ax2 + bx + c = 0 then the product of the roots is c/a.
What form is the solving for the roots of quadratic equations?
Using the quadratic equation formula or completing the square
How do you formulate quadratic equation that can be solve by extracting square roots?
By using the quadratic equation formula
