Equation: kx^2 +x^2 +kx +k +1 = 0 Using the discriminant: K^2 -4*(k +1)*(k +1) = 0 Expanding brackets: k^2 -4k^2 -8k -4 = 0 Collecting like terms: -3^2 -8k -4 = 0 Dividing all terms by -1: 3k^2 +8k +4 = 0 Factorizing the above: (3k +2)(k +2) = 0 meaning k = -2/3 or -2 Therefore possible values of k are either: -2/3 or -2
If the equation has equal roots then the discriminant of b^2 -4ac = 0:- Equation: kx^2 +x^2 +kx +k +1 = 0 Discriminant: k^2 -4(k+1)(k+1) = 0 Multiplying out brackets: k^2 -4k^2 -8k -4 = 0 Collecting like terms: -3k^2 -8k -4 = 0 Divide all terms by -1: 3k^2 +8k +4 = 0 Factorizing: (3k +2)(k +2) = 0 => k = -2/3 or k = -2 Therefore possible values of k are -2/3 or -2
If: 6x^2 +2x +k = 0 has equal roots Then using the discriminant of b^2 -4ab=0: 4 -24k=0 => k=-4/-24 => k=1/6 Therefore the value of k = 1/6
Equation: 2kx^2 -2x^2 +2kx +k -1 = 0 Using the discriminant: (2k)^2 -4*(2k -2)*(k -1) = 0 Solving for k in the discriminant: k = 2 + or - square root of 2
Equation: x^2 +2kx +10x +k^2 +5 = 0 Using the discriminant: (2k +10)^2 -4*1*(k^2 +5) = 0 Solving the discriminant: k = -2
(k - 1)(k + 1)(k - 2)(k + 2)
k=4
K/3 + k/4 = 1 LCD=12 *divide lcd by denominator* K(4) + K(3) = 12(1) 4k + 3k = 12 7k = 12 k=12/7
Equation: kx^2 +x^2 +kx +k +1 = 0 Using the discriminant: K^2 -4*(k +1)*(k +1) = 0 Expanding brackets: k^2 -4k^2 -8k -4 = 0 Collecting like terms: -3^2 -8k -4 = 0 Dividing all terms by -1: 3k^2 +8k +4 = 0 Factorizing the above: (3k +2)(k +2) = 0 meaning k = -2/3 or -2 Therefore possible values of k are either: -2/3 or -2
If the equation has equal roots then the discriminant of b^2 -4ac = 0:- Equation: kx^2 +x^2 +kx +k +1 = 0 Discriminant: k^2 -4(k+1)(k+1) = 0 Multiplying out brackets: k^2 -4k^2 -8k -4 = 0 Collecting like terms: -3k^2 -8k -4 = 0 Divide all terms by -1: 3k^2 +8k +4 = 0 Factorizing: (3k +2)(k +2) = 0 => k = -2/3 or k = -2 Therefore possible values of k are -2/3 or -2
If: 6x^2 +2x +k = 0 has equal roots Then using the discriminant of b^2 -4ab=0: 4 -24k=0 => k=-4/-24 => k=1/6 Therefore the value of k = 1/6
Yes, they are exactly the same, both of them increment k in 1.
If: y = 3x +1 then y^2 = 9x^ +6x +1 If: x^2 +y^2 = k then 10^x^2 +6x +(1-k) = 0 Using the discriminant: -4 +40k = 0 Add 4 to both sides: 40k = 4 Divide both sides by 40: k = 1/10 Therefore the value of k is 1/10
0
Equation: 2kx^2 -2x^2 +2kx +k -1 = 0 Using the discriminant: (2k)^2 -4*(2k -2)*(k -1) = 0 Solving for k in the discriminant: k = 2 + or - square root of 2
12 - 4 + k = 85 8 + k = 85 k = 77
Equation: x^2 +2kx +10x +k^2 +5 = 0 Using the discriminant: (2k +10)^2 -4*1*(k^2 +5) = 0 Solving the discriminant: k = -2