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Solve 3x2-2x2 using the quadratic formula Exopress your answer in simplest radical form?
Do you mean 3x = 2 - 2x^2 ?
3x = 2 - 2x^2
3x - 2 + 2x^2 = 2 - 2x^2 -2 + 2x^2
2x^2 + 3x - 2 = 0
a = 2, b = 3, c = -2 (a, b, and c are real numbers)
The quadratic formula is:
x = [-b + & - square root of(b^2 - 4ac)]/2a, so
x = [-3 + & - square root of(3^2 - (4)(2)(-2)]/(2)(2)
x = [-3 + & - square root of(9 + 16)]/4
x = (-3 + & - square root of 25)/4
x = (-3 + & - 5)/4
x = (-3 + 5)/4 = 2/4 = 1/2 or
x = (-3 - 5)/4 = -8/4 = -2
The roots of the equation are -2 and 1/2.
The quantity that appears beneath the radical sign in the quadratic formula, b^2 - 4ac, is called the discriminant, which can tell you whether the roots of quadratic equation are real or imaginary.
If b^2 - 4ac = 0, there is one real root, called the double root.
If b^2 - 4ac > 0, there are two different real roots.
If b^2 - 4ac < 0, there are two conjugate imaginary roots.
What else can I help you with?
What is the Simplest radical form of the square root of 13?
That IS the simplest radical form.
What is the simplest radical form of 112?
4radical7
When is written in simplest radical form which value remains under the radical?
The radicand is the value under the radical symbol.
What is the simplest radical form of 208?
4*SQRT(13)
What is the square root of 32 in simplest radical form?
4√2
The is the name of the number under the radical symbol in the quadratic formula?
discriminant
What is the name of the number under the radical symbol in the quadratic formula?
The discriminant
What is the expression b2 4ac under the radical sign in the quadratic formula?
The discriminant.
Why do imaginary answers occur in quadratic equations?
imaginary numbers occur in the quadratic formula because of the radical symbol, and the possibility of a negative radican and that results in imaginary numbers. I hope this helped!
What is the difference between a radical equation and a quadratic equation?
radical equations have sq roots, cube roots etc. Quadratic equations have x2.
Can X equal a negative radical using the quadratic formula?
Yes any time 4ac > b2 then x will be a complex numberthe curve represented by that formula will have no x intercepts.Yes.
How do you factor the trinomial x2 plus 4x minus 10?
I assume you mean x(squared) + 4x - 10. Solving this isn't extremely difficult if you know the quadratic formula. first of all, remember the form ax(squared) + bx + c you are currently in that form. so, the formula is (-b +OR- radical(b(squared) - 4ac)) /2a so, using the formula, you will get (-4 + or - radical(16 - 4(1)(-10)))/2(1) this simplifies to (-4 + or - radical(56)) / 2 this can simplify to (-4 + or - radical(4) * radical(14)) / 2 the 2 in the denominator cancels out with the -4 and the 2(comes from radical(4)) in the numerator. this leaves us with -2 + or - radical(14) these are the two solutions. x= -2 + radical(14) x = -2 - radical(14) this may seem complex since it's hard to explain in this way, but I promise you will understand it. here is an easier to understand version of the quadratic formula.
What is the simplest radical for of 53?
It's already in simplest radical form.
What is the Simplest radical form of the square root of 13?
That IS the simplest radical form.
When is a radical in simplest form?
when there is no radical in the denominator
How do you solve complex cases of quadratic equations?
If the discriminant - the part under the radical sign in the quadratic formula - is negative, then the result is complex, it is as simple as that. You can't convert a complex number to a real number. If a particular problem requires only real-number solutions, then - if the formula gives complex numbers - you can state that there is no solution.
What is an easy way to go the quadratic formula?
the quadratic formula is really complex. so, if you can avoid it, you should. one way i do this is by getting the trinomial into X^2 - 2YX + Y^2 = 0 form. here's an example lets say we have x^2 - 2x - 5 = 0 normally we would have to do the quadratic formula however, if we get it into this form, we can get x^2 - 2(1)x + 1 = 6 all i did was add 6 to both sides of the equation. you can now simplify the left side of the equation, and be left with (x-1)^(2) = 6 to get ride of the exponent on the left side, find the square root of both sides. this will leave you with (x-1) = (+ or -)radical(6) add one to both sides and you will get x = 1 (+ or -)radical(6) therefore, x can equal 1 + radical(6) or 1 - radical(6) now, this may seem complex, but it is easy once you get used to it. It is far more efficient than the long quadratic formula.
