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6 is the mean proportion between two numbers x and y and 48 is the third proportional of x and y. Find the numbers.
Concept: Proportion
If x, y, z are in continued proportion, prove that `(x + y)^2/(y + z)^2 = x/z`
Concept: Proportion
The following numbers, K + 3, K + 2, 3K – 7 and 2K – 3 are in proportion. Find k.
Concept: Proportion
Using properties of proportion solve for x, given
`(sqrt(5x)+sqrt(2x -6))/(sqrt(5x)- sqrt(2x -6)) = 4`
Concept: Ratio
The mean proportional between 4 and 9 is ______.
Concept: Proportion
What number must be added to each of the numbers 4, 6, 8, 11 in order to get the four numbers in proportion?
Concept: Proportion
If `(a + b)^3/(a - b)^3 = 64/27`
- Find `(a + b)/(a - b)`
- Hence using properties of proportion, find a : b.
Concept: Proportion
What must be subtracted from 16x3 – 8x2 + 4x + 7 so that the resulting expression has 2x + 1 as a factor?
Concept: Remainder Theorem
Using remainder theorem, find the value of k if on dividing 2x3 + 3x2 – kx + 5 by x – 2, leaves a remainder 7.
Concept: Remainder Theorem
If (x + 2) and (x + 3) are factors of x3 + ax + b, find the values of ‘a’ and ‘b’.
Concept: Factor Theorem
Use Remainder theorem to factorize the following polynomial:
`2x^3 + 3x^2 - 9x - 10`
Concept: Remainder Theorem
Find 'a' if the two polynomials ax3 + 3x2 – 9 and 2x3 + 4x + a, leaves the same remainder when divided by x + 3.
Concept: Remainder Theorem
Using the Remainder and Factor Theorem, factorise the following polynomial:
`x^3 + 10x^2 - 37x + 26`
Concept: Remainder Theorem
A two digit positive number is such that the product of its digits is 6. If 9 is added to the number, the digits interchange their places. Find the number.
Concept: Applications of Factor Theorem
If (x – 2) is a factor of the expression 2x3 + ax2 + bx – 14 and when the expression is divided by (x – 3), it leaves a remainder 52, find the values of a and b.
Concept: Factor Theorem
Using the Remainder Theorem, factorise the following completely:
3x3 + 2x2 – 19x + 6
Concept: Remainder Theorem
Find the value of ‘k’ if (x – 2) is a factor of x3 + 2x2 – kx + 10. Hence determine whether (x + 5) is also a factor.
Concept: Factor Theorem
When divided by x – 3 the polynomials x3 – px2 + x + 6 and 2x3 – x2 – (p + 3) x – 6 leave the same remainder. Find the value of ‘p’.
Concept: Applications of Factor Theorem
Use the Remainder Theorem to factorise the following expression:]
`2x^3 + x^2 - 13x + 6`
Concept: Remainder Theorem
Using the factor theorem, show that (x - 2) is a factor of `x^3 + x^2 -4x -4 .`
Hence factorise the polynomial completely.
Concept: Applications of Factor Theorem
