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on dividing the polynomial 4x4 - 5x3 - 39x2 - 46x - 2 by the polynomial gx the quotient is x2 - 3x - 5 and the remainder is -5x 8find the polynomial
if alpha beta are the zeros of the polynomial x2 8x 6 frame a quadratic polynomial whose zeros are a 1alpha and 1beta b 1 betaalpha 1
if alphabeta are the zeros of the polynomial 2x2 - 4x 5 find the value of a alpha2 beta2 b alpha - beta2ans p x 2 x2 - 4 x
find the quadratic polynomial whose sum and product of zeros are radic2 1 1 radic2 1ans sum 2 radic2product 1qp x2 - sum x
find the greatest number of 6 digits exactly divisible by 24 15 and 36 ans999720ans lcm of 24 15 36lcm 3 times 2 times 2 times 2 times 3 times 5
show that for odd positive integer to be a perfect square it should be of the form8k 1 let a2m1ans squaring both sides we get a2 4m m 1 1there4
show that the product of 3 consecutive positive integers is divisible by 6ansnn1n2 be three consecutive positive integerswe know that n is of the
if d is the hcf of 30 72 find the value of x amp y satisfying d 30x 72yans5 -2 not uniqueans using euclids algorithm the hcf 30 7272
show that 571 is a prime numberans let x571rarrradicxradic571now 571 lies between the perfect squares of 232 and 242prime numbers
find the least number that is divisible by all numbers between 1 and 10 both inclusiveans the required number is the
find the largest possible positive integer that will divide 398 436 and 542 leaving remainder 7 11 15 respectivelyans 17ans the required number is
prove that one of every three consecutive integers is divisible by 3ansnn1n2 be three consecutive positive integerswe know that n is of the form 3q
express the gcd of 48 and 18 as a linear combination ans not uniqueabqr where o le r lt
number systems numbers are intellectual witnesses that belong only to mankindexampleif the h c f of 657 and 963 is
verify liouville3939393939393939s formula for y quot-yquot - y3939393939393939 y 0 in 0 1
next we have to talk about evaluating functions evaluating a function is in fact nothing more than asking what its value is for particular values
now we need to move onto something called function notation function notation will be utilized heavily throughout most of remaining section and
example find out which of the following equations functions are amp which are not
a function is an equation for which any x which can be plugged into the equation will yield accurately one y out of the equationthere it is ie the
the following relation is not a function 610 -7 3 0 4 6 -4solutiondont
a function is a relation for which each of the value from the set the first components of the ordered pairs is related with exactly one value from
definition of a functionnow we need to move into the second topic of this chapter before we do that however we must look a quick definition taken
example write down the equation of a circle alongwith radius 8 amp center -4 7 solutionokay in this case we have r 8 h -4 and k 7
perpendicular to the line given by 10 y 3x -2for this part we desire the line to be perpendicular to 10 y 3x -2 amp so we know we can determine the
parallel to the line specified by 10 y 3x -2in this case the new line is to be parallel to the line given by 10 y 3x -2 and so it have to have the