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جستجوهای پرتکرار

میتونی لایو بذاری!

The polynomial $f\left( x \right)$ is defined by

$f\left( x \right) = 12{x^3} + 25{x^2} - 4x - 12$.

a) Show that $f\left( { - 2} \right) = 0$ and factorise $f\left( x \right)$ completely.

b) Given that

$12 \times {27^y} + 25 \times {9^y} - 4 \times {3^y} - 12 = 0$,

state the value of ${3^y}$ and hence find $y$ correct to 3 significant figures.

پاسخ تشریحی :
نمایش پاسخ

a) Verify that $ - 96 + 100 + 8 - 12 = 0$

Attempt to find quadratic factor by division by $\left( {x + 2} \right)$, reaching a partial quotient $12{x^2} + kx$, inspection or use of an identity

Obtain $12{x^2} + x - 6$

State $\left( {x + 2} \right)\left( {4x + 3} \right)\left( {3x - 2} \right)$

[The M1 can be earned if inspection has unknown factor $A{x^2} + Bx - 6$ and an equation in $A$ and/or $B$ or equation $12{x^2} + Bx + C$ and an equation in $B$ and/or $C$.]

b) State ${3^y} = \frac{2}{3}$ and no other value

Use correct method for finding y from equation of form ${3^y} = k$, where $k \gt 0$

Obtain –0.369 and no other value $ - 0.369$

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