گاما رو نصب کن!

{{ number }}
اعلان ها
اعلان جدیدی وجود ندارد!
کاربر جدید

جستجو

پربازدیدها: #{{ tag.title }}

جستجوهای پرتکرار

میتونی لایو بذاری!

The polynomial $\alpha {x^3} + b{x^2} + 5x - 2$, where $\alpha $ and $b$ are constants, is denoted by $p\left( x \right)$. It is given that $\left( {2x - 1} \right)$ is a factor of $p\left( x \right)$ and that when $p\left( x \right)$ is divided by $\left( {x - 2} \right)$ the remainder is 12.

a) Find the values of $\alpha $ and $b$.

b) When $\alpha $ and $b$ have these values, find the quadratic factor of $p\left( x \right)$.

پاسخ تشریحی :
نمایش پاسخ

a) Substitute $x = \frac{1}{2}$ and equate to zero, or divide, and obtain a correct equation, e.g.

$\frac{1}{8}\alpha  + \frac{1}{4}b + \frac{5}{2} - 2 = 0$

Substitute $x = 2$ and equate result to 12, or divide and equate constant remainder to 12

Obtain a correct equation, e.g. $8\alpha  + 4b + 10 - 2 = 12$

Solve for $\alpha $ or for $b$

Obtain $\alpha  = 2$ and $b =  - 3$

b) Attempt division by $2x - 1$ reaching a partial quotient $\frac{1}{2}\alpha {x^2} + kx$

Obtain quadratic factor ${x^2} - x + 2$

[The M1 is earned if inspection has an unknown factor $A{x^2} + Bx + 2$ and an equation in $A$ and/or $B$, or an unknown factor of $\frac{1}{2}\alpha {x^2} + Bx + C$ and an equation in $B$ and/or $C$.]

تحلیل ویدئویی تست

تحلیل ویدئویی برای این تست ثبت نشده است!