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What are the possible values of k when kx2 plus x2 plus kx plus k plus 1 equals 0 has repeated roots?
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
What are the possible values of k when the curve of kx squared plus x squared plus kx plus k plus 1 equals 0 has equal roots?
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
What is the value of k when the equation of 6x squared plus 2x plus k equals 0 has equal roots?
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
What are the possible values of k when 2kx2 -2x2 plus 2kx plus k -1 equals 0 has equal roots?
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
What is the value of k when x2 plus 2kx plus 10x plus k2 plus 5 equals 0 has equal roots?
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
