§5. Dấu của tam thức bậc hai
Các câu hỏi tương tự
Lập bảng xét dấu các biểu thức sau :
a. \(f\left(x\right)=\left(3x^2-10x+3\right)\left(4x-5\right)\)
b. \(f\left(x\right)=\left(3x^2-4x\right)\left(2x^2-x-1\right)\)
c. \(f\left(x\right)=\left(4x^2-1\right)\left(-8x^2+x-3\right)\left(2x+9\right)\)
d. \(f\left(x\right)=\dfrac{\left(3x^2-x\right)\left(3-x^2\right)}{4x^2+x-3}\)
Bài 1: xét dấu tam thức bậc hai
1.f(x)= -1/2 x^2
2.f(x)=x^2-2x-1
3.v=-x^2-4x+1
4.v=x^2+x+1
5.v=-x^2+4x+6
6.y= căn bặc hai 2x^2
7.y=((1-căn bậc hai 2)x^2-2x-1
8.v=2(x+3)^2-5
9.v= trừ căn bậc hai 2^2+4x
xét dấu các biểu thức:
a) f(x)=(4x-1)(x+2)(3x-5)
b)f(x)= \(\frac{9}{x+2}-2\)
c)f(x)= \(\frac{x^2+2x+5}{x+1}-\left(x-3\right)\)
Bài 3 : Xét dấu biểu thức sau :
1 , fleft(xright)frac{x-7}{4x^2-19x+12}
2 , fleft(xright)frac{11x+3}{-x^2+5x-7}
3 , fleft(xright)frac{3x-2}{x^3-3x^2+2}
4 , fleft(xright)frac{x^2+4x-12}{sqrt{6}x^2+3x+sqrt{2}}
5 , fleft(xright)frac{x^2-3x-2}{-x^2+x-1}
6 , fleft(xright)frac{x^3-5x+4}{x^4-4x^3+8x-5}
7 , fleft(xright)frac{left(x+3right)left(x-2right)left(-2x^2+x-1right)}{left(2x-5right)left(x^2+3x-10right)}
8 , fleft(xright)left(-x^2+x-1right)left(6x^2-5x+1right)
9 , fleft(xright)frac{x^2-...
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Bài 3 : Xét dấu biểu thức sau :
1 , \(f\left(x\right)=\frac{x-7}{4x^2-19x+12}\)
2 , \(f\left(x\right)=\frac{11x+3}{-x^2+5x-7}\)
3 , \(f\left(x\right)=\frac{3x-2}{x^3-3x^2+2}\)
4 , \(f\left(x\right)=\frac{x^2+4x-12}{\sqrt{6}x^2+3x+\sqrt{2}}\)
5 , \(f\left(x\right)=\frac{x^2-3x-2}{-x^2+x-1}\)
6 , \(f\left(x\right)=\frac{x^3-5x+4}{x^4-4x^3+8x-5}\)
7 , \(f\left(x\right)=\frac{\left(x+3\right)\left(x-2\right)\left(-2x^2+x-1\right)}{\left(2x-5\right)\left(x^2+3x-10\right)}\)
8 , \(f\left(x\right)=\left(-x^2+x-1\right)\left(6x^2-5x+1\right)\)
9 , \(f\left(x\right)=\frac{x^2-x-2}{-x^2+3x+4}\)
10 , \(f\left(x\right)=\left(x^2-5x+4\right)\left(2-5x+2x^2\right)\)
Bài 2 Xét dấu biểu thức sau
1 , fleft(xright)x^2-sqrt{3}x+frac{3}{4}
2 , fleft(xright)-x^2+3x-2
3 , fleft(xright)x^4-4x+1
4 , fleft(xright)frac{3x+7}{x^2-x-2}
5 , fleft(xright)frac{x+2}{3x+1}-frac{x-2}{2x-1}
6 , fleft(xright)frac{1}{x^2-5x+4}-frac{1}{x^2-7x+10}
7 , fleft(xright)left(x-1right)left(x-3right)-frac{18}{x^2-4x-4}
8 , fleft(xright)left(x^2-1right)left(x-2right)
9 , fleft(xright)left(x+3right)left(-4x^2+9x-2right)
10 , fleft(xright)frac{10-x}{5+x^2}-frac{1}{2}
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Bài 2 Xét dấu biểu thức sau
1 , \(f\left(x\right)=x^2-\sqrt{3}x+\frac{3}{4}\)
2 , \(f\left(x\right)=-x^2+3x-2\)
3 , \(f\left(x\right)=x^4-4x+1\)
4 , \(f\left(x\right)=\frac{3x+7}{x^2-x-2}\)
5 , \(f\left(x\right)=\frac{x+2}{3x+1}-\frac{x-2}{2x-1}\)
6 , \(f\left(x\right)=\frac{1}{x^2-5x+4}-\frac{1}{x^2-7x+10}\)
7 , \(f\left(x\right)=\left(x-1\right)\left(x-3\right)-\frac{18}{x^2-4x-4}\)
8 , \(f\left(x\right)=\left(x^2-1\right)\left(x-2\right)\)
9 , \(f\left(x\right)=\left(x+3\right)\left(-4x^2+9x-2\right)\)
10 , \(f\left(x\right)=\frac{10-x}{5+x^2}-\frac{1}{2}\)
Bài 1 Xét dấu biểu thức sau
1 , fleft(xright)2x^2-x+1
2 , fleft(xright)-2x^2+5x+7
3 , fleft(xright)9x^2-12x+4
4 , fleft(xright)2x^2+2x+5
5 , fleft(xright)2x^2+2sqrt{2}x+1
6 , fleft(xright)-4x^2-4x+1
7 , fleft(xright)sqrt{3}x+left(sqrt{3}+1right)x+1
8 , fleft(xright)x^2+left(sqrt{5}-1right)x-sqrt{5}
9 , fleft(xright)x^2-left(sqrt{7}-1right)+sqrt{3}
10 , fleft(xright)left(1-sqrt{2}right)x^2-2x+1+sqrt{2}
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Bài 1 Xét dấu biểu thức sau
1 , \(f\left(x\right)=2x^2-x+1\)
2 , \(f\left(x\right)=-2x^2+5x+7\)
3 , \(f\left(x\right)=9x^2-12x+4\)
4 , \(f\left(x\right)=2x^2+2x+5\)
5 , \(f\left(x\right)=2x^2+2\sqrt{2}x+1\)
6 , \(f\left(x\right)=-4x^2-4x+1\)
7 , \(f\left(x\right)=\sqrt{3}x+\left(\sqrt{3}+1\right)x+1\)
8 , \(f\left(x\right)=x^2+\left(\sqrt{5}-1\right)x-\sqrt{5}\)
9 , \(f\left(x\right)=x^2-\left(\sqrt{7}-1\right)+\sqrt{3}\)
10 , \(f\left(x\right)=\left(1-\sqrt{2}\right)x^2-2x+1+\sqrt{2}\)
Giải các bft
a. \(x^2-2\left(1+\sqrt{2}\right)x+3+2\sqrt{2}>0\)
b. \(\frac{3x^2-10x+3}{x^2+4x+4}\ge0\)
Bài 4 Xét dấu biểu thức sau
1 , fleft(xright)x^2-3x-2-frac{8}{x^2-3x}
2 , fleft(xright)frac{1}{x+1}-frac{1}{x}-frac{1}{2}
3 , fleft(xright)frac{x^2-4x+3}{3-2x}-1+x
4 , fleft(xright)frac{x^2-1}{left(x^2-3right)left(-3x^2+2x+8right)}
5 , fleft(xright)x^4-5x^2+2x+3
6 , fleft(xright)frac{x^2+4x+15}{x^2-1}-frac{x-3}{x+1}-frac{x-2}{1-x}
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Bài 4 Xét dấu biểu thức sau
1 , \(f\left(x\right)=x^2-3x-2-\frac{8}{x^2-3x}\)
2 , \(f\left(x\right)=\frac{1}{x+1}-\frac{1}{x}-\frac{1}{2}\)
3 , \(f\left(x\right)=\frac{x^2-4x+3}{3-2x}-1+x\)
4 , \(f\left(x\right)=\frac{x^2-1}{\left(x^2-3\right)\left(-3x^2+2x+8\right)}\)
5 , \(f\left(x\right)=x^4-5x^2+2x+3\)
6 , \(f\left(x\right)=\frac{x^2+4x+15}{x^2-1}-\frac{x-3}{x+1}-\frac{x-2}{1-x}\)
Xét dấu biểu thức:
f(x) = \(\frac{\left(x^2-4x+\text{4}\right)\left(x^2+5x+\text{4}\right)}{4x^2-x-3}\)