Mathematics
Assertion (A) : 25x2 - 5x + 1 is a perfect square trinomial.
Reason (R) : Any trinomial which can be expressed as x2 + y2 + 2xy or x2 + y2 - 2xy is a perfect square trinomial.
Both A and R are correct, and R is the correct explanation for A.
Both A and R are correct, and R is not the correct explanation for A.
A is true, but R is false.
A is false, but R is true.
Factorisation
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Answer
(5x - 1)2 = (5x)2 - 2.5x.1 + 12
= 25x2 - 10x + 12
Thus, 25x2 - 5x + 1 is not a perfect square trinomial.
So, assertion (A) is false.
(x - y)2 = x2 - 2.x.y + y2
= x2 - 2xy + y2
And, (x + y)2 = x2 + 2.x.y + y2
= x2 + 2xy + y2
Thus, x2 + y2 + 2xy or x2 + y2 - 2xy is a perfect square trinomial.
So, reason (R) is true.
Hence, option 4 is the correct option.
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Related Questions
a(x - y)2 - by + bx is equal to :
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(x - y) (ax + by - b)
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(x - y) (ax - ay + b)
Statement 1: The product of two binomials is a trinomial, conversely if we factorise a trinomial we always obtain two binomial factors
Statement 2: The square of the difference of two terms = the sum of the same two terms x their difference.
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= x2 + (4 + 3)x + 3 x 4
= x2 + 4x + 3x + 3 x 4
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Both A and R are correct, and R is not the correct explanation for A.
A is true, but R is false.
A is false, but R is true.
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Reason (R) : (x + a) (x + b) = x2 + (a + b)x + ab.
Both A and R are correct, and R is the correct explanation for A.
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