1a)If the quadratic equation kx2+(2k+3)x+(k+6)=0 has a double real root and k is a constant,find the value of k.
1b) From the result of (a),solve the equation kx2+(2k+3)x+(k+6)=0
2a)It is given that k is a non-zero constant.Express the discriminant of the quadratic equation kx2+(k+3)x+3=0 in terms of k
2b)Prove that the equation has real roots.
要有步驟thx
幾條中四math題(急10分)
2009-10-04 7:49 pm
回答 (1)
2009-10-04 8:02 pm
✔ 最佳答案
1.a. kx2 + (2k + 3)x + (k + 6) = 0 has a double real root.Discriminant = 0
(2k + 3)2 - 4k(k + 6) = 0
4k2 + 12k + 9 - 4k2 - 24k = 0
k = 3/4
b. The equation becomes:
3/4 x2 + [2(3/4) + 3]x + (3/4 + 6) = 0
x2 + 6x + 9 = 0
(x + 3)2 = 0
x = -3
2.a. kx2 + (k + 3)x + 3 = 0
Discriminant = (k + 3)2 - 4k(3)
= k2 + 6k + 9 - 12k
= k2 - 6k + 9
= (k - 3)2
b. As the discriminant = (k - 3)2 >= 0
So, the equation has real roots.
參考: Physics king
收錄日期: 2021-04-19 16:02:01
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