Mathematics
Assertion (A) : There are two values of b so that x2 + bx - 24 is factorisable.
Reason (R) : Two values have:
Product = -24 and sum = 2.
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
Given: x2 + bx - 24
To factor such a quadratic, we look for two numbers that :
Multiply to get −24 (the constant term)
Add to b (the coefficient of the middle term)
Values of b such that their sum is 2 and product is -24 are 6 and -4.
So, reason (R) is true.
⇒ x2 + bx - 24
⇒ x2 + 6x - 4x - 24
⇒ x(x + 6) - 4(x + 6)
⇒ (x - 4)(x + 6)
So, assertion (A) is true and reason clearly explains assertion (A).
Hence, option 1 is the correct option.
Answered By
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Related Questions
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.
Assertion (A) : The value of k so that the factors of are same is .
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.
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.
Factorise :
6x3 - 8x2
Factorise :
36x2y2 - 30x3y3 + 48x3y2