If the system of equtions `px+by+cz=0, ax+qy+cz=0, ax+by+rz=0` has a non - trivial solution and `pneq, qnebb, r nec`, prove that `(p)/(p-a)+(q)/(q-b)+(r)/(r-c)=2`.

If the system of linear equations x + 2ay + az = 0 , x + 3by + bz = 0 , x + 4cy + cz = 0 has a non-zero solution, then a, b, c

If the system of linear equation x + 2ay + az = 0, x + 3by + bz = 0, x + 4cy + cz = 0 has a non-trival solution then show that a, b, c are in H.P.

If p q r!=0 and the system of equation (p+a)x+b y-c z=0 a x+(q+b)y+c z=0 a c+b y+(r+c)z=0 has nontrivial solution, then value of 1/p+b/q+c/r is -1 b. 0 c. 0"" d. not-2

If p q r!=0 and the system of equation (p+a)x+b y+c z=0 a x+(q+b)y+c z=0 a x+b y+(r+c)z=0 has nontrivial solution, then value of a/p+b/q+c/r is -1 b. 0 c. 0"" d. not-2

Let alpha_1,alpha_2 and beta_1, beta_2 be the roots of the equation ax^2+bx+c=0 and px^2+qx+r=0 respectively. If the system of equations alpha_1y+alpha_2z=0 and beta_1y_beta_2z=0 has a non trivial solution then prove that b^2/q^2=(ac)/(pr)

Statement 1: If b c+q r=c a+r p=a b+p q=-1, t h e n|a p a p b q b q c r c r|=0(a b c ,p q r!=0)dot Statement 2: if system of equations a_1x+b_1y+c_1=0,a_2x+b_2y+c_2=0,a_3x+b_2y+c^3=0 has non -trivial solutions |a_1b_1c_1a_2b_2c_2a_3b_3c_3|=0

Three lines px + qy+r=0, qx + ry+ p = 0 and rx + py + q = 0 are concurrent of

If a!=p ,b!=q ,c!=ra n d|p b c a q c a b r|=0, then find the value of p/(p-a)+q/(q-b)+r/(r-c)dot

If ax^2 + bx + c = 0, a, b, c in R has no real zeros, and if a + b + c + lt 0, then