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
0
12 - 4 + k = 85 8 + k = 85 k = 77
If: y = kx+1 and y = 3x2-4x+4 Then: 3x2-4x+4 = kx+1 So: 3x2-4x-kx+3 = 0 For the line to be tangent to the curve the discriminant of b2-4ac must = 0 So when: -4*3*3 = -36 then (-4-k)2 must = 36 So it follows: (-4-k)(-4-k) = 36 => k2+8k-20 = 0 Solving the quadratic equation: k = 2 or k = -10
neg(-k) + neg(-k) = k + k = 2k = 4
50
#include<stdio.h> #include<conio.h> void main() { int i,j,k=0,l; clrscr(); for(i=1;i<=5;i++) { for(j=1;j<=i;j++) { k++; printf("%d ",k%2); } for(l=i;l<=4;l++) { k++; } printf("\n"); } getch(); }
k=8k+28 k-8k=28 -7k=28 k=-(28/4) k=-4
1 + 1 + 1 + 1/4 + 5/5 = 4 and 1/4
2 k^2 - k - 4 = 0 2 (k^2 - (1/2)k - 2) = 0 2 ((k - 1/4)^2 - 1/16 - 2) = 0 2 ((k - 1/4)^2 - 33/16) = 0 2 (k - 1/4 - sqrt(33)/4)(k - 1/4 + sqrt(33)/4) = 0 32 (4k - 1 - sqrt(33))(4k - 1 + sqrt(33)) = 0