If your function is 4x^2+16x+16=0 then x=-2, if it is 4x^2-16x+16=0, then x=2
2*2 - 12x +16 =0 4 - 12x +16 =0 -12x + 16 +4 =0 -12x + 20 =0 -12x = -20 x = 1.666666667
2 mod 5 is the remainder left when 2 is divided by 5.2 = 5*0 + 2 so [the quotient is 0 and] the remainder is 2that is 2 mod 5 = 2.On spreadsheets, the formula is usually "=MOD(2,5)"
6x - 2 = 16 : 6x = 16 + 2 = 18 : x = 18÷ 6 = 3 :x - 3 = 3 - 3 = 0 : x - 3 = 0
15 times 6 = 90
If your function is 4x^2+16x+16=0 then x=-2, if it is 4x^2-16x+16=0, then x=2
1 + 1 = 0 in binary. Why does this happen?Note: Adding binary numbers is related to modulo 2 arithmetic.Let's review mod and modular arithmetic with addition.modulus 2 is the mathematical term that is the remainder from the quotient of any term and 2. For instance, if we have 3 mod 2, then we have 3 / 2 = 1 + ½. The remainder is 1. So 3 ≡ 1 mod 2.What if we want to add moduli?The general form is a mod n + b mod n ≡ (a + b) mod n.Now, for the given problem, 1 mod 2 + 1 mod 2 ≡ 2 mod 2. Then, 2 mod 2 ≡ 0 mod 2.Therefore, 1 + 1 = 0 in binary.
2*2 - 12x +16 =0 4 - 12x +16 =0 -12x + 16 +4 =0 -12x + 20 =0 -12x = -20 x = 1.666666667
2 mod 5 is the remainder left when 2 is divided by 5.2 = 5*0 + 2 so [the quotient is 0 and] the remainder is 2that is 2 mod 5 = 2.On spreadsheets, the formula is usually "=MOD(2,5)"
x*x - 8x +16 = 0 x*x = 8x + 16 x - 16 = _/8x x_/-4 = 2 x = 2
x = -2 and y = 0
3x2 + 2x = 16 ∴ 3x2 + 2x - 16 = 0 ∴ 3x2 - 6x + 8x - 16 = 0 ∴ 3x(x - 2) + 8(x - 2) = 0 ∴ (3x + 8)(x - 2) = 0 ∴ x ∈ {-8/3, 2}
We see that we must find a number n such that it satisfies the condition: n ≡ 0 (mod 2) ≡ 0 (mod 3) ≡ 0 (mod 9) Since 9 is a multiple of 3, we can forget about the 0 (mod 3). Since 2 and 9 are relatively prime, the Chinese Remainder Theorem states that there indeed exists a number n such that it satisfies n ≡ 0 (mod 2) ≡ 0 (mod 9). Now let 2K represent some multiple of 2, and set it congruent to 0 (mod 9): 2K ≡ 0 (mod 9) This is a particularly easy case; 2K would have to equal some multiple of 9 for it to satisfy this expression. Therefore, K = 9 and n must = 18c, where c is an arbitrary multiplier. This is your new modulus: n ≡ 0 (mod 18) Any n that satisfies this condition will also satisfy n ≡ 0 (mod 2) ≡ 0 (mod 3) ≡ 0 (mod 9).
m2 - 8m + 16 = 0 (m - 4)2 = 0 so m = 4
6x - 2 = 16 : 6x = 16 + 2 = 18 : x = 18÷ 6 = 3 :x - 3 = 3 - 3 = 0 : x - 3 = 0
256 128 64 32 16 8 4 2 1 1 0 0 0 1 0 0 1 1 256, 16, 2, 1 add them together is 275 Answer is 275
2(x - 2)(x + 4) = 0 x = 2, -4