Assertion A : 3 x 2 - 16 x + 4 - 16 is satisfied for some values of real x in 0 , 10 3 . Reason R : a x 2 + b x + c and a will have the same sign for some values of x ∈ R when b 2 - 4 a c 0 . The correct option among the following is

Question

Assertion A : 3 x 2 - 16 x + 4 > - 16 is satisfied for some values of real x in 0 , 10 3 . Reason R : a x 2 + b x + c and a will have the same sign for some values of x ∈ R when b 2 - 4 a c > 0 . The correct option among the following is, A is true, R is true and R is the correct explanation for A, A is true, R is true but R is not the correct explanation for A, A is true, but R is false, A is false, but R is true

MARKS App · Accepted Answer

Given that 3 x 2 - 16 x + 20 = f x here a = 3 , b = - 16 & c = 20 a > 0 & D = b 2 - 4 a c = 256 - 240 > 0 f x > 0 ⇒ 3 x 2 - 16 x + 20 > 0 ⇒ 3 x - 10 x - 2 > 0 ⇒ x ∈ - ∞ , 2 ∪ 10 3 , ∞ . Hence, A is false, but R is true

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