the are no real roots?
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Explanation: If a quadratic equation has no real roots then its discriminant is less than zero. The discriminant of general quadratic equation ax2+bx+c=0 is b2−4ac .
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There is NO solution, so any non-zero number divided by 0 is undefined. Comment on CarlBiologist's post “Infinity is not a real number, and even if it were...”
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Zero has one square root which is 0. ... The square roots of numbers that are not a perfect square are members of the irrational numbers. This means that they can't be written as the quotient of two integers. The decimal form of an irrational number will neither terminate nor repeat.
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No BUT --- ALL REAL numbers ARE COMPLEX numbers. It just so happens that many complex numbers have 0 as their imaginary part.
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If the discriminant is equal to zero, this means that the quadratic equation has two real, identical roots. Therefore, there are two real, identical roots to the quadratic equation x2 + 2x + 1. D > 0 means two real, distinct roots.
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A differentiable function f(x) has no turning points if its derivative f′(x) has no real roots. f′(x)=3x2+2ax+b, so the equation 3x2+2ax+b=0 should have no roots.
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The square root of a negative number does not exist among the set of Real Numbers.
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The points at which the graph crosses or touches x- axis, give the real roots of the function (or zeros of the function) represented by the graph. If the graph touches x-axis and turns back, then it would be a double root at that point.
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And so a/b must be an integer. This proof shows that what we said about square roots extends to cube roots and in fact to all integer roots. For example, the fifth root of an integer is either an integer or an irrational number.
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The definitions are as follows if a unique non negative solution exists for the equation then it can be called as principal root. ... For example, the principal root of x2=4 is 2. The real valued root are on the other hand is a set of all roots of the equation which are real.
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(See Algebraic closure and Fundamental theorem of algebra.) The term "imaginary" is used because there is no real number having a negative square. There are two complex square roots of −1, namely i and −i, just as there are two complex square roots of every real number other than zero, which has one double square root.
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What is the square root of negative infinity? ... Yes, and , so the square roots of are . You can compactify the complex numbers by adding a point at infinity in every direction, so for every nonzero complex number there is a point , and we have if and are positive real multiples of one another.
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Gollum: What has roots as nobody sees, is taller than trees, up, up, up it goes, and yet, never grows? 2. Bilbo: Thirty white horses on a red hill.
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If the discriminant of a quadratic function is less than zero, that function has no real roots, and the parabola it represents does not intersect the x-axis.
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When complex nth roots are considered, it is often useful to choose one of the roots as a principal value. The common choice is the one that makes the nth root a continuous function that is real and positive for x real and positive.
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The lack of features, such as a multi-layered epidermis or bark, means that non-vascular plants don't grow very tall and typically remain low to the ground. As such, they don't need a vascular system to transport water and nutrients. ... Genuine leaves, stems, and roots are all missing in non-vascular plants.
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There are no absolute continuums. There are no surfaces. There are no straight lines.” If we look at a high-altitude image of salt flats, deserts, rocks, and any number of other things from nature we might see what appear to be reasonably straight lines here and there at different resolutions.