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the length of the sides of a triangle are 2x y2 5x3 y 12 and 23 x 2y 52 if the triangle is equilateral find its perimeterans 2x y2 4x
the given fact will relate all of these ideas to the multiplicity of the zerofactif x r is a zero of the polynomial p x along with multiplicity k
the humps where the graph varies direction from increasing to decreasing or decreasing to increasing is frequently called turning points if we
in this section we are going to look at a technique for getting a violent sketch of a general polynomial the only real information which were going
a chemist has one solution which is 50 acid and a second which is 25 acid how much of each should be mixed to make 10 litres of 40 acid
factor theoremfor the polynomial p x 1 if value of r is a zero of p x then x - r will be a factor of p x 2 if x - r is a factor of p x then r
if p x is a polynomial of degree n then p x will have accurately n zeroes some of which might repeatthis fact says that if you list out all the
list the multiplicities of the zeroes of each of the following polynomials p x 5x5 - 20x4 5x3
a train covered a certain distance at a uniform speed if the train would have been 6kmhr faster it would have taken 4hours less than the
now weve got some terminology to get out of the waymultiplicity k if r is a zero of a polynomial and the exponent on the term that produced the
example determine the zeroes of following polynomialsp x 5x5 - 20x45x3 50x2 - 20x - 40 5 x 12 x - 23solutionin this the factoring has been done
the larger of two supplementary angles exceeds the smaller by 180 find them ans990810ans x y 1800 x - y
well begin this section by defining just what a root or zero of a polynomial is we say that x r is a root or zero of a polynomial p x if p r
students are made to stand in rows if one student is extra in a row there would be 2 rows less if one student is less in a row there would be 3 rows
find the value of p and q for which the system of equations represent coincident lines 2x 3y 7 pq1x p2q2y 4pq1ans a1 2 b1 3 c1 7a2 p q
given a polynomial px along degree at least 1 amp any number r there is another polynomial qx called as the quotient with degree one less than
41x 53y 135 53x 41y 147ans 41x 53 y 135 53 x 41 y 147add the two equations solve it to get x y 3 -------1 subtract solve it to
a2bx 2a- by 2 a - 2bx 2a by 3ans 5b - 2a10ab a 10b10ab ans2ax 4ay y we get 4bx - 2by -12ax 4ay 5 4bx- 2by - 1solve this to
7y 3 - 2x 2 14 4 y - 2 3x - 3 2ans 7y 3 - 2 x 2 14 --------- 14y- 2 3x - 3 2 ----------2from
solve for x yx y - 82 x 2 y - 143 3x y - 1211 ans x2 y6ans x y - 82 x 2y - 14 3
pair of linear equations in two variables like the crest of a peacock so is mathematics at the head of all
actually we will be seeing these sort of divisions so frequently that wed like a quicker and more efficient way of doing them luckily there is
if the ratios of the polynomial ax33bx23cxd are in ap prove that 2b3-3abca2d0ans let px ax3 3bx2 3cx
1 determine the intercepts if there are any recall that the y-intercept is specified by0 f 0 and we determine the x-intercepts by setting the
if alpha amp szlig are the zeroes of the polynomial 2x2 - 4x 5 then find the value of aalpha2 szlig2 b 1 alpha 1 szlig c alpha - szlig2 d