Show, by the method of contradiction `:`
p `: ` If `x ` is a real number such that `x^(3) + 8 x = 0 `, then ` x = 0` .

Show that the statement: p: If x is a real number such that x^(3)+x=0, then x is 0 is true by Dirtect method ii.number of contrapostive Method of contradition

Show that the statement p: "If x is a real number such that x^3+4x=0 . then x is 0" is true by (i) direct method, (ii) method of contradiction, (iii) method of contrapositive.

Show that the statement: p:Ifx is a real number such that x^(3)J=4x=0, the x is 0 is true by Direct method ii.method of contradiction ii.method of contrapositive

Consider the statement : p : If x a real number such that x^3 +4x =0 then x=0 prove that p is a true statement using : (i) direct method d (ii) method of contradiction (iii) method of contrapositive

If a is defined by f (x)=a_(0)x^(n)+a_(1)x^(n-2)+a_(2)x^(n-2)+...+a_(n-1)x+a_(n) where n is a non negative integer and a_(0),a_(1),a_(2),…….,a_(n) are real numbers and a_(0) ne 0, then f is called a polynomial function of degree n. For polynomials we can define the following theorem (i) Remainder theorem: Let p(x) be any polynomial of degree greater than or equal to one and 'a' be a real number. if p(x) is divided by (x-a), then the remainder is equal to p(a). (ii) Factor theorem : Let p(x) be a polynomial of degree greater than or equal to 1 and 'a' be a real number such that p(a) = 0, then (x-a) is a factor of p(x). Conversely, if (x-a) is a factor of p(x). then p(a)=0. The factor of the polynomial x^(3)+3x^(2)+4x+12 is

Check the validity of the statements given below by the method given against it.(i) p: The sum of an irrational number and a rational number is irrational (by contradiction method).(ii) q: If n is a real number with n>3 then (by contradiction method).

The number of real roots of x^(8) - x^(5) + x^(2) - x + 1 = 0 is

The number of real root of the equal x^(3) -6x +9 = 0 is :

The number of real solutions of x^(2) - 3|x| + 2 = 0 is