Question

Відповідь. 24. Які з виразів набувають тільки від'ємних значень при будь-якому значенні х:а) - х? - 4х +6; б) - x2 + 16x — 64; в) - x2 + 8x - 18;1) а,б,в: 2) а,б: 3) б.в: 4) а.в: 5) a; б) в: 7) інша відповідь.​

Answer 1

Ответ:

інша відповідь,Ответ:только б.

Answer 2

Expressions with Only Negative Values for Any Value of x

When considering the expressions in question, we need to determine which ones will always have negative values for any value of x. Let's analyze each expression:

a) -x - 4x + 6 b) -x^2 + 16x - 64 c) -x^2 + 8x - 18

To determine if an expression will always have negative values, we can look at the leading coefficient and the discriminant of the quadratic expression.

1. Expression a) -x - 4x + 6: - The leading coefficient is -1, which means the parabola opens downwards. - Since the coefficient of x^2 is 0, this expression is not a quadratic equation. - Therefore, this expression does not have a consistent sign and can have positive or negative values depending on the value of x.

2. Expression b) -x^2 + 16x - 64: - The leading coefficient is -1, which means the parabola opens downwards. - The discriminant is 16^2 - 4(-1)(-64) = 256 - 256 = 0. - Since the discriminant is zero, the quadratic equation has a single real root. - Therefore, this expression will always have negative values for any value of x.

3. Expression c) -x^2 + 8x - 18: - The leading coefficient is -1, which means the parabola opens downwards. - The discriminant is 8^2 - 4(-1)(-18) = 64 - 72 = -8. - Since the discriminant is negative, the quadratic equation has no real roots. - Therefore, this expression will always have negative values for any value of x.

Based on the analysis above, expressions b) and c) will always have negative values for any value of x. Therefore, the correct answer is б) -x^2 + 16x - 64 and в) -x^2 + 8x - 18.