Show that: `|x p q p x q q q x|=(x-p)(x^2+p x-2q^2)dot`

Show that: x p q p x q q q xx-p)(x^2+p x-2q^2) .

Using properties of determinants, show that |{:(x, p, q), ( p, x, q), (q,q,x):}|= (x-p) (x ^(2) + px - 2q ^(2))

Show that Delta={:|(x,p,q),(p,x,q),(q,q,x)| = (x-p)(x^2+px-2q^2)

Show that |(x,p,q),(p,x,x),(q,q,x)| = (x - p)(x^(2) + px - 2q^2)

Prove that |(x,p,q),(p,x,q),(p,q,x)| = (x - p)(x - q)(x + p +q)

If the lines p_1 x + q_1 y = 1, p_2 x + q_2 y=1 and p_3 x + q_3 y = 1 be concurrent, show that the points (p_1 , q_1), (p_2 , q_2 ) and (p_3 , q_3) are colliner.

If the equation x^2 + px + q =0 and x^2 + p' x + q' =0 have common roots, show that it must be equal to (pq' - p'q)/(q-q') or (q-q')/(p'-p) .

If p ,q are real p!=q , then show that the roots of the equation (p-q)x^2+5(p+q)x-2(p-q)=0 are real and unequal.

If p,q are real p!=q, then show that the roots of the equation (p-q)x^(2)+5(p+q)x-2(p-q)=0 are real and unequal.

Given that q^2-p r ,0,\ p >0, then the value of |p q p x+q y q r q x+r y p x+q y q x+r y0| is- a. zero b. positive c. negative \ d. q^2+p r