If both ` (x-2) and (x - (1)/(2))` are fractors of `p x ^(2) +5x +r,` then show that p=r.

Find the relation between p and r if (x - 2) and (x-1/2) be two factors of the polynomial px^(2)+5x+r .

If x = a - (1)/(a), y = b - (1)/(b) and z = c - (1)/(c ) and a, b, c are in G.P., then show that (x+z)/(y) = r + (1)/(r ) , where r is the common ratio of the G.P.

If the p^(th) , q^(th) and r^(th) terms of a G.P. are x , y , z respectively. then show that : x^(q-r) . y^(r-p).z^(p-q)=1

If the ratio of the roots of a x ^2+2b x+c=0 is same as the ratio of roots of p x^2+2q x+r=0, then a. (2b)/(a c)=(q^2)/(p r) b. b/(a c)=(q^2)/(p r) c. (b^2)/(a c)=(q^2)/(p r) d. none of these

Three points P (h, k), Q(x_(1) , y_(1))" and " R (x_(2) , Y_(2)) lie on a line. Show that (h - x_(1)) (y_(2) - y_(1)) = (k - y_(1)) (x_(2) - x_(1)) .

5/(x-1)gt2,xne1 and x in R

If the coefficients of r^("th"),(r+1)^("th")and(r+2)^("th") terms in the expansion of (1+x)^(14) are in A.P ., then r is /are -

If x^2+p x+q=0a n dx^2+q x+p=0,(p!=q) have a common roots, show that 1+p+q=0 .

Let a(a != 0) is a fixed real number and (a-x)/(p x) = (a-y)/(qy) = (a-z)/(r z) . If p, q, r are in A.P., show that (1)/(x), (1)/(y), (1)/(z) are in A.P.

If p(x)=3x^(4)-5x^(3)+x^(2)+8 , then p(1) =