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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 , are the roots of 3x – 2x – 3 = 0, find the values of

, 是 3x – 2x – 3 = 0 的根, 求值

[a]

[b]

[c]

(a)

(b)

(c)

[2]

The equation 3x + 10x + p = 0, has roots and where = 2 , find the value of p.

3
[3]

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

,
[4]

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

[5]

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

[a] ,

[b] ,

(a) 8x – 18x + 13 = 0

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

[6]

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

[7]

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

6, -3
[8]

Given that and are the roots of the equation 2x = 3x – 4,

[a]

form an equation whose roots are and .

[b]

show that 4 = – 12.