If each pair ofthe following three equations x: `x^2+p_1x + q_1 =0`.`x^2 + p_2x +q_2=0` , `x^2+p_3x+q_3=0` , has exactly one root common, prove that `(p_1+p_2+p_3)^2=4(p_1p_2+p_2p_3+p_3p_1-q_1-q_2-q_3]`

If each pair ofthe following three equations x: x^(2)+p_(1)x+q_(1)=0.x^(2)+p_(2)x+q_(2)=0x^(2)+p_(3)x+q_(3)=0, has exactly one root common, prove that (p_(1)+p_(2)+p_(3))^(2)=4(p_(1)p_(2)+p_(2)p_(3)+p_(3)p_(1)-q_(1)-q_(2)-q_(3)]

If 2,3 are the roots of the equation 2x^3+px^2-13x+q=0 then (p,q) is

If p and q are roots of the equation 2x^2-7x+3 then p^2+q^2=

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 p and q are the roots of the equation x^2-p x+q=0 , then p=1,\ q=-2 (b) b=0,\ q=1 (c) p=-2,\ q=0 (d) p=-2,\ q=1

If p and q are the roots of the equation x^2 - 15x + r = 0 and. p - q = 1 , then what is the value of r?

If p(q-r)x^(2)+q(r-p)x+r(p-q)=0 has equal roots,then prove that (2)/(q)=(1)/(p)+(1)/(r)

Solve the following system of equations.(x)/(p)+(y)/(q)=1p(x-p)-q(y+q)=2p^(2)+q^(2)