Thus `f(0)=f(1)` and hence equation `f\'(x)=0` has at least one root between 0 and 1. Show that equation `(x-1)^5+(2x+1)^9+(x+1)^21=0` has exactly one real root.

Show that the equation (x-1)^5+(x+2)^7+(7x-5)^9=10 has exactly one root.

Prove that the equation 3x^(5)+15x-18=0 has exactly one real root.

The equation kx^(2)+x+k=0 and kx^(2)+kx+1=0 have exactly one root in common for

If the equation x^(3) - 3x + a = 0 has distinct roots between 0 and 1, then the value of a is

If the cubic equation 3x^3 +px +5=0 has exactly one real root then show that p gt 0

Find the condition if the equation 3x^2+4a x+b=0 has at least one root in (0,1)dot

Find the condition if the equation 3x^2+4a x+b=0 has at least one root in (0,1)dot

If 2a+3b+6c = 0, then show that the equation a x^2 + bx + c = 0 has atleast one real root between 0 to 1.

If 2a+3b+6c = 0, then show that the equation a x^2 + bx + c = 0 has atleast one real root between 0 to 1.

Statement-1: Let a,b,c be non zero real numbers and f(x)=ax^2+bx+c satisfying int_0^1 (1+cos^8x)f(x)dx=int_0^2(1+cos^8x)f(x)dx then the equation f(x)=0 has at least one root in (0,2) .Statement-2: If int_a^b g(x)dx vanishes and g(x) is continuous then the equation g(x)=0 has at least one real root in (a,b) . (A) Both 1 and 2 are true and 2 is the correct explanation of 1 (B) Both 1 and 2 are true and 2 is not correct explanation of 1 (C) 1 is true but 2 is false (D) 1 is false but 2 is true