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Assertion (A): One root of x^3 - 2x^2 -1...

Assertion (A): One root of `x^3 - 2x^2 -1 = 0` lies between 2 and 3 Reason (R): If `f(x)` is continuous function and f(a),f(b), have oppsite signs then atleast one (or) odd number of roots of `f(x) = 0` lies between a and b

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If f(x) is a continuous function and attains only rational values and f(0) = 3 , then roots of equation f(1)x^2 +f(3)x+f(5)=0 as

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Let alpha be the root of the equation ax^2+bx+c=0 and beta be the root of the equation ax^2-bx-c=0 where alphaltbeta Assertion (A): Equation ax^2+2bx+2c=0 has exactly one root between alpha and beta ., Reason(R): A continuous function f(x) vanishes odd number of times between a and b if f(a) and f(b) have opposite signs. (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true R is not te correct explanation of A (C) A is true but R is false. (D) A is false but R is true.

Let alpha be the root of the equation ax^2+bx+c=0 and beta be the root of the equation ax^2-bx-c=0 where alphaltbeta Assertion (A): Equation ax^2+2bx+2c=0 has exactly one root between alpha and beta ., Reason(R): A continuous function f(x) vanishes odd number of times between a and b if f(a) and f(b) have opposite signs.

Assertion (A): For 0ltaltbltc equation (x-a)(x-b)-c=0 has no roots in (a,b) Reason (R):For a continuous function f(x) equation f\'(x)=0 has at least one root between a and b if f(a) and f(b) are equal. (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true R is not the correct explanation of A (C) A is true but R is false. (D) A is false but R is true.

Assertion (A): For 0ltaltbltc equation (x-a)(x-b)-c=0 has no roots in (a,b) , Reason (R):For a continuous function f(x) equation f\'(x)=0 has at least one root between a and b if f(a) and f(b) are equal. (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true R is not the correct explanation of A (C) A is true but R is false. (D) A is false but R is true.

If f is continuous function at x=0, where f(x)=((2^(x)+3^(x))/(2))^((2)/(x)), then f(0) is one of the roots of the equation