4. For what value of k, will the equation 2kx? - 2(1 + 2k)x + (3 + 2k)

1.	4. For what value of k, will the equation 2kx? - 2(1 + 2k)x + (3 + 2k) = 0 have real butdistinct roots? When will the roots be[CBSE 2010]
Answer» for real and distinct root we must have D>0 I.e. b^2-4ac>0so use -2(1+2k) as b , 2k as a and 3+2k as c condition for equal root b^2-4ac= 0{2(1+2k)^2-4(2k)(3+2k=04(1+4k+4k^2)= 4(6k+ 4k^2)1+4k+4k^2= 6k+4k^211= 6k-4k1= 2k1/2=k equal root b^2-4ac; [2(1+2k)^2-4(2k)(3+2k)=0; 4(1+4k+4k^2]=4[6k+4k^2); 1+4k+4k^2=6k+4k^2; 1+ 4k=6k; 1=6k-4k=2k; k=1/2

4. For what value of k, will the equation 2kx? - 2(1 + 2k)x + (3 + 2k) = 0 have real butdistinct roots? When will the roots be[CBSE 2010]

Answer»

for real and distinct root we must have D>0 I.e. b^2-4ac>0so use -2(1+2k) as b , 2k as a and 3+2k as c

condition for equal root b^2-4ac= 0{2(1+2k)^2-4(2k)(3+2k=04(1+4k+4k^2)= 4(6k+ 4k^2)1+4k+4k^2= 6k+4k^211= 6k-4k1= 2k1/2=k

equal root b^2-4ac; [2(1+2k)^2-4(2k)(3+2k)=0; 4(1+4k+4k^2]=4[6k+4k^2); 1+4k+4k^2=6k+4k^2; 1+ 4k=6k; 1=6k-4k=2k; k=1/2