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.
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.
Related Questions
a(x - y)2 - by + bx is equal to :
(x - y) (ax + by + b)
(x - y) (ax + by - b)
(x - y) (x + y + a - b)
(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.
Which of the following options is correct?
Both the statements are true.
Both the statements are false.
Statement 1 is true, and statement 2 is false.
Statement 1 is false, and statement 2 is true.
Assertion (A) : x2 + 7x + 12
= x2 + (4 + 3)x + 3 x 4
= x2 + 4x + 3x + 3 x 4
= (x + 4)(x + 3)
Reason (R) : To factorise a given trinomial, the product of the first and the last term of the trinomial is always the sum of the two parts when we split the middle term.
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.