Tìm nghiệm của đa thức
A) A = 5x – 125
B) B = x² + 3x – 18
C) C = 8x² + 30x + 7
D) D = x² + 6x – 7
E) E = x³ – 11x² + 30x
Mn giúp em với ạ ^^
Tìm nghiệm của đa thức A) A = 5x – 125 B) B = x² + 3x – 18 C) C = 8x² + 30x + 7 D) D = x² + 6x – 7 E) E = x³ – 11x² + 30x Mn giúp em với ạ ^^
By Samantha
`A=5x-125`
`⇒5x-125=0`
`⇔5x=125`
`⇔x=25`
`B=x^2+3x-18`
`⇒x^2+3x-18=0`
`⇔x^2-6x+3x-18=0`
`⇔x(x-6)+3(x-6)=0`
`⇔(x+3)(x-6)=0`
`⇔` \(\left[ \begin{array}{l}x+3=0\\x-6=0\end{array} \right.\) `⇔` \(\left[ \begin{array}{l}x=-3\\x=6\end{array} \right.\)
`C=8x^2+30x+7`
`⇒8x^2+30x+7=0`
`⇔8x^2+28x+2x+7=0`
`⇔4x(2x+7)+(2x+7)=0`
`⇔(4x+1)(2x+7)=0`
`⇔` \(\left[ \begin{array}{l}4x+1=0\\2x+7=0\end{array} \right.\) `⇔` \(\left[ \begin{array}{l}x=\dfrac{-1}{4}\\x=\dfrac{-7}{2}\end{array} \right.\)
`D=x^2+6x-7`
`⇒x^2+6x-7=0`
`⇔x^2+7x-x-7=0`
`⇔x(x+7)-(x+7)=0`
`⇔(x-1)(x+7)=0`
`⇔` \(\left[ \begin{array}{l}x-1=0\\x+7=0\end{array} \right.\) `⇔` \(\left[ \begin{array}{l}x=1\\x=-7\end{array} \right.\)
`E=x^3-11x^2+30x`
`⇒x^3-11x^2+30x=0`
`⇔x(x^2-11x+30)=0`
`⇔x(x^2-6x-5x+30)=0`
`⇔x[x(x-6)-5(x-6)]=0`
`⇔x(x-5)(x-6)=0`
`⇔x=0; x = 5; x = 6`
Đáp án:
Giải thích các bước giải:
$5x-125=0$
$⇔5(x-25)=0$
$⇔x-25=0$
$⇔x=25$
$x^2+3x-18=0$
$⇔x^2+6x-3x-18=0$
$⇔(x-3)(x+6)=0$
⇔\(\left[ \begin{array}{l}x=3\\x=-6\end{array} \right.\)
$8x^2+30x+7=0$
$⇔8x^2+2x+28x+7=0$
$⇔(2x+7)(4x+1)=0$
⇔\(\left[ \begin{array}{l}2x=-7\\4x=-1\end{array} \right.\)
⇔\(\left[ \begin{array}{l}x=-\dfrac{7}{2}\\x=-\dfrac{1}{4}\end{array} \right.\)
$x^2+6x-7=0$
$⇔x^2+7x-x-7$
$⇔(x-1)(x+7)=0$
⇔\(\left[ \begin{array}{l}x=1\\x=-7\end{array} \right.\)
$x^3-11x^2+30x=0$
$⇔x^3-5x^2-6x^2+30x=0$
$⇔x^2(x-5)-6x(x-5)=0$
$⇔x(x-6)(x-5)=0$
⇔\(\left[ \begin{array}{l}x=0\\x=6\\x=5\end{array} \right.\)