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Lesson List
第四章:部分分式 Partial Fraction
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第六章:角的形成及单位 Angles and Measurements
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第十三章: 方程组 Simultaneous Equations
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第十五章:二元一次不等式及线性规划 linear inequality in two variables and linear programming
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Lesson: 2.3 一元二次方程式的根与系数的关系 The Relations of Roots and Coefficients of Quadratic Equations
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2.3 The Relations of Roots and Coefficients of Quadratic Equations 一元二次方程式的根与系数的关系


 

[1]

If \alpha, \beta are the roots of 3x^2 – 2x – 3 = 0, find the values of

\alpha, \beta 是 3x^2 – 2x – 3 = 0 的根, 求值

[a] \frac{1}{\alpha}+\frac{1}{\beta}

[b] \alpha^2 + \beta^2

[c] \frac{\beta}{\alpha}+\frac{\alpha}{\beta}

Answer:
(a) \frac{2}{3}

(b) 2\frac{4}{9}

(c) -2\frac{4}{9}

[2]

The equation 3x^2 + 10x + p = 0, has roots \alpha and \beta where \alpha\beta = 2\frac{2}{3} , find the value of p.

方程式3x^2 + 10x + p = 0 有根 \alpha\beta 其中 \alpha\beta = 2\frac{2}{3} , 求 p的值.

Answer:
3
[3]

The equation 2x^2 – 2x + 3 = 0 has roots p and q and the equation x^2 – x + 2m = 0 has roots and . Find the values of k and m.

方程式2x^2 – 2x + 3 = 0 有根 p 和 q 及方程式 x^2 – x + 2m = 0 有根 和 . 求 k 和 m的值.

Answer:
1\frac{1}{2} , \frac{3}{4}
[4]

If the square of the difference of the roots of equation x^2 – mx +15 = 0 is 4, find the value of m.

若方程式x^2 – mx +15 = 0 的根的平方差是 4, 求 m 的值.

Answer:
\pm 8
[5]

If \alpha and \beta are the roots of equation 2x^2– 3x+ 4 = 0, find the equation whose roots are

\alpha\beta 是方程式2x^2– 3x+ 4 = 0 的根, 求作方程式其根是

[a] \alpha+\frac{1}{\alpha} , \beta+\frac{1}{\beta}

[b] \alpha^2 , \beta^2

Answer:
(a) 8x^2 – 18x + 13 = 0

(b) 4x^2 + 7x + 16 = 0

[6]

One root of the equation 2x^2 – x + c = 0 is twice the other. Find the value of c.

方程式2x^2 – x + c = 0 其中一根是另外一根的两倍. 求 c的值.

Answer:
\frac{1}{9}
[7]

One root of the equation 3x^2 – 3px + p^2 = p + 6 is twice of the other. Find the values of p.

方程式3x^2 – 3px + p^2 = p + 6 其中一根是另外一根的一半. 求 p的值.

Answer:
6, -3
[8]

Given that \alpha and \beta are the roots of the equation 2x^2 = 3x – 4,

已知 \alpha\beta 是方程式 2x^2 = 3x – 4的根,

[a]

form an equation whose roots are \alpha\beta and \beta\alpha.

作方程式其根是\alpha\beta and \beta\alpha.

[b]

show that 4\alpha^3 = \alpha – 12.

证明4\alpha^3 = \alpha – 12.

Answer:
(a) 4x^2 + 23 = 0
Exercise Files
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Lesson List
第四章:部分分式 Partial Fraction
0/1
第六章:角的形成及单位 Angles and Measurements
0/1
第十三章: 方程组 Simultaneous Equations
0/1
第十五章:二元一次不等式及线性规划 linear inequality in two variables and linear programming
0/2
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