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## Finding big remainder in a small way (Tomato objective 288 )

Problem: The remainder R(x) obtained by dividing the polynomial by the polynomial is (A) (B) (C) (D) SOLUTION:  (B) The the divisor is a quadratic term .So, R(x) must be 1 degree less than divisor. We know , when , when , solving two equation we get, and, The...

## Condition of real roots (Tomato objective 291)

Problem: If the roots of the equation ${(x-a)(x-b)}+{(x-b)(x-c)}+{(x-c)(x-a)}=0$,(where a,b,c are real numbers) are equal , then (A) $b^2-4ac=0$ (B) $a=b=c$ (C)  $a+b+c=0$ (D)    none of  foregoing statements is correct   Answer: ans (B) ...

## Real Roots of a Cubic Polynomial (TOMATO Objective 258)

Problem:Let a,b,c be distinct real numbers.Then the number of real solution of is (A) 1 (B) 2 (C) 3 (D) depends on a,b,c Solution: Ans: (A) Let But it is not possible a quadratic equation has three roots.so, it implies that  f'(x) has no real roots.But  f(x) is a...

## Roots of a Quintic Polynomial (TOMATO Objective 257)

Problem: The number of real roots of is (A) 0 (B) 3 (C) 5 (D) 1   Solution:  Answer: (D) The expression in underline doesn’t have any real roots. Therefore, only real root of the equation is ...