S1 : Let a,b,c ∈ C and ax2 + bx + c = 0 be a quadratic equation. Then b2 -4ac = 0 ⇒ roots are real and equal.

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Consider the following statements :

S1 : Let a,b,c  C and ax2 + bx + c = 0 be a quadratic equation. Then b2 -4ac = 0  roots are real and equal.

S2 : Let b,c  I and b2 - 4c be a perfect square. Then roots of the equation x2 + bx + c = 0 may not be integers.

S3 : If the quadratic equations a1x2 + b1x + c1 = 0 and a2x2+ b2x + c2 = 0 have common root, then a1/a2 = b1/b2 = c1/c2.

S4 : f(x) = a1x2 + b1x + c1 /a2x2+ b2x + c2 , g (x) = lx + m/ax + b

where a1 , a2 , l , a are non zero real and other coefficients are also real. Then range of f(x)  range of g(x). State, in order, whether S1 , S2 , S3 , S4 are true or false

(A) TTFT

(B)  TTTF

(C)  FFTT

(D)  FFFF

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Correct option (D) FFFF

Explanation:

S1 : D = 0  roots are real and equal if a, b, c  R.

S2 : Roots are integers

S3 : a1/a2 = b1/b2 = c1/cis true iff roots are both common

S4 : If Numerator and Denominator have common factor then Rf can be equal to Rg .