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

Find the value of k, if x-1 is a factor of p(x) in each of the following cases : p(x) = 2x^(2) + kx + sqrt(2)

Find the value of k, if x-1 is a factor of p(x) in each of the following cases : p(x) = kx^(2) - sqrt(2)x + 1

Let p,q,r be roots of cubic x^(3)+2X^(2)+3x+3=0 , then

Let for a != a_1 != 0 , f(x)=ax^2+bx+c , g(x)=a_1x^2+b_1x+c_1 and p(x) = f(x) - g(x) . If p(x) = 0 only for x = -1 and p(-2) = 2 then the value of p(2) .

Inequality 3(x-1) + 2 (x-2) lt 5 (x +2) is true for each x in R .

Inequality 3(x-1) + 2 (x-2) lt 5 (x +2) is true for each x in R .

if the roots of the equation 1/ (x+p) + 1/ (x+q) = 1/r are equal in magnitude but opposite in sign, show that p+q = 2r & that the product of roots is equal to (-1/2)(p^2+q^2) .

Let R be the set of real numbers. If f: R to R ;f(x)=x^2 and g: R to R ;g(x)=2x+1 . Then, find fog and gof . Also, show that fog!=gofdot

Verify whether the values of x given in each case are the zeroes of the polynomial or not ? (i) p (x) = 2 x + 1,x =- 1/2 (ii) p (x) = 5x -pi , x = (-3)/(2) (iii) p (x) = x ^(2) -1 , x = pm 1 (iv) p (x) = (x-1) (x +2) , x =-1,k-2 (v) p (y) = y ^(2) , y =0 (vi ) p (x) = ax + b, x =- (b)/(a) (vii) f (x) = 3x ^(2) -1 , x =- (1)/(sqrt3) , (2)/(sqrt3) (viii) f (x) =2x -1 , x = (1)/(2), (-1)/(2)