Question

(i) `4x^2 - 5sqrt(2)x - 7 = (2sqrt(2)x + 7)(sqrt(2)x - 1)`

(ii) x² + x + px + p = (x + 1)(x + p)

पर्याय

• Only (i)

• Only (ii)

• Both (i) and (ii)

• Neither (i) nor (ii)

Answer 1

Only (ii)

Explanation:

(i) The expression `4x^2 - 5sqrt(2)x - 7` can be factorized as:

`4x^2 - 5sqrt(2)x - 7 = (2sqrt(2)x + 7)(sqrt(2) x - 1)`

This matches the given factorization exactly.

(ii) The expression x² + x + px + p factors as:

x² + x + px + p = x² + (1 + p)x + p

If factored as (x + 1)(x + p) = x² + (p + 1)x + p, it matches the above only if (p) is a constant and the middle term is (p + 1)x.

Since the given expression has (x + px), which is x(1 + p), the factorization is correct only if (p) is a constant.

The expression x² + x + px + p is equivalent to (x + 1)(x + p).

This confirms (ii) is also a valid factorization.