`` If teeth are moved too rapidly, serious injury can be done to their roots as well as to the surrounding bone holding them in place '', explains Dr. Brodie.

If the quadratic polynomial is monic then the roots are quadratic integers.

If < math > c ^ 2 < 4km </ math > there are two complex conjugate roots a ± ib, and the solution ( with the above boundary conditions ) will look like this:

* If f is an irreducible polynomial of prime degree p with rational coefficients and exactly two non-real roots, then the Galois group of f is the full symmetric group S < sub > p </ sub >.

If un-aerated, the solution level is kept low enough that enough roots are above the solution so they get adequate oxygen.

If too much water and not enough air surrounds the plants roots, it is possible to gradually lower the medium's water-retention capability by mixing in increasing quantities of perlite.

A number a is a root of P if and only if the polynomial x − a ( of degree one in x ) divides P. It may happen that x − a divides P more than once: if ( x − a )< sup > 2 </ sup > divides P then a is called a multiple root of P, and otherwise a is called a simple root of P. If P is a nonzero polynomial, there is a highest power m such that ( x − a )< sup > m </ sup > divides P, which is called the multiplicity of the root a in P. When P is the zero polynomial, the corresponding polynomial equation is trivial, and this case is usually excluded when considering roots: with the above definitions every number would be a root of the zero polynomial, with undefined ( or infinite ) multiplicity.

If the equation lacks a constant term a < sub > 0 </ sub >, then 0 is one of the rational roots of the equation.

If the latter is too hard, the roots will not penetrate it readily and, as a result, the plant will be pushed up and out of the earth during the process of growth.

If the name has an Indo-European etymology, it is possibly a suffixed form of a root * wel-" to turn, roll ", or of * sel-" to flow, run ".< ref > The American Heritage Dictionary, " Indo-European roots: wel < sup > ₂ </ sup >"</ ref > The latter possibility would allow comparison to the Vedic Sanskrit Saraṇyū, a character who is abducted in Rigveda 10. 17. 2.

If no grasses are available, mud or roots unearthed from marsh beds are employed.

* If P ( x ) is a primitive polynomial which has integer coefficients but is not monic, and P is irreducible over Q, then none of the roots of P are algebraic integers.

If the matrix being factorized is positive definite as required, the numbers under the square roots are always positive in exact arithmetic.

If the roots r < sub > 1 </ sub >, r < sub > 2 </ sub >, ... are all distinct, then the solution to the recurrence takes the form

Different solutions are obtained depending on the nature of the roots: If these roots are distinct, we have the general solution

) If g ( x ) = 1, then p ( x ) has no multiple roots and we can safely use those other root-finding algorithms which work best when there are no multiple roots, and then exit.

If degree ( Q ) ≤ 4 then the multiple roots of P may be found algebraically.

Given an algebraically closed field A containing K, there is a unique splitting field L of p between K and A, generated by the roots of p. If K is a subfield of the complex numbers, the existence is automatic.

If left in the ground, the texture tends to become woody, but the storage life of untreated whole roots is not long.

If n is even and the number is real and positive, one of its nth roots is positive, one is negative, and the rest are complex but not real ; if n is even and the number is real and negative, none of the nth roots are real.

If it were not for an old professor who made me read the classics I would have been stymied on what to do, and now I understand why they are classics ; ;

If I even hint at it do you think it will matter that you are his nephew -- and not even a blood nephew ''??

If the circumstances are faced frankly it is not reasonable to expect this to be true.

If his dancers are sometimes made to look as if they might be creatures from Mars, this is consistent with his intention of placing them in the orbit of another world, a world in which they are freed of their pedestrian identities.

If love reflects the nature of man, as Ortega Y Gasset believes, if the person in love betrays decisively what he is by his behavior in love, then the writers of the beat generation are creating a new literary genre.

If to be innocent is to be helpless, then I had been -- as are we all -- helpless at the start.

Defoe then commented, `` If they Could Draw that young Gentleman into Their Measures They would show themselves quickly, for they are not asham'd to Say They want only a head to Make a beginning ''.

If Jews are identified as a religious body in a controversy that comes before a national or international tribunal, it is obviously compatible with the goal of human dignity to protect freedom of worship.

If they are right, they will prevail of and by themselves.

Without preliminaries, Esther asked him, `` If you are a world citizen, will you take Garry Davis' place in his tent while he goes to the hospital ''??

If we are to believe the list of titles printed in Malraux's latest book, La Metamorphose Des Dieux, Vol. 1 ( ( 1957 ), he is still engaged in writing a large novel under his original title.

If the would-be joiner asks these questions he is not likely to be duped by extremists who are seeking to capitalize on the confusions and the patriotic apprehensions of Americans in a troubled time.

If we break the minister to our bit, we are buying back our own sins.

If the record buyer's tastes are somewhat eclectic or even the slightest bit esoteric, he will find them satisfied on educational records.

If Daddy's books are out of bounds his own picture books are not.

If it will simply delay the debates until the qualifications are closed next spring, and then carry all the candidates on a tour of debates, it can provide a service to the state.

If they are to be commended for foresight in their planning, what then is the judgment of a town council that compounds this problem during the planning stage??

If the Communists are sincere in wanting a united, neutral and disarmed Germany, it might well be advantageous for the German people in this nuclear age.

If only this could be done more often -- with such heartening results -- many of the earth's `` big problems '' would shrink to the insignificances they really are.

If any are left, presently, we may expect to see signs specifically prohibiting the feeding of them too.

If the raw population figures are crucially relevant, then it is idle to think of liberation, as idle as to suppose that Poland might liberate Russia.

If it is not enough that all of our internationalist One Worlders are advocating that we join this market, I refer you to an article in the New York Times' magazine section ( Nov. 12, 1961 ), by Mr. Eric Johnston, entitled `` We Must Join The Common Market ''.

If the UN troops are not mercenaries then the Hessians were not mercenaries either.