1. It is given that the quadratic equation 4x^2-2(2k+1)x+9=0 has two equal real roots.
(a) Find the possible value(s) of k.
(b) When k is negative in (a), solve the equation.
2. It is given that the graph of y=(m-2)x^2+(2m+5)x+(m+1) cuts the x-axis at two points.
(a) Determine whether the value of m can be 2. Explain your answer.
(b) Find range of possible value(s) of m.
F4 Nature of roots
2011-10-13 4:44 am
回答 (2)
2011-10-13 7:07 am
✔ 最佳答案
1(a)the quadratic equation has two equal real rootsdelta=0
(-2(2k+1))^2-4(4)(9)=0
4(2k+1)^2-144=0
(2k+1)^2=36
2k+1=+/-6
k=5/2 or -7/2
(b)4x^2-2(2(-7/2)+1)x+9=0
4x^2+12x+9=0
(2x+3)^2=0
x=-3/2
2(a)no.
sub m=2
y=(2-2)x^2+(2*2+5)x+(2+1)
y=9x+3
it is not a quadratic equation.
(b)the graph cuts the x-axis at two points
delta>0
(2m+5)^2-4(m-2)(m+1)>0
4m^2+20m+25-4(m^2-m-2)>0
4m^2+20m+25-4m^2+4m+8>0
24m+33>0
m>-11/8 and m=/=2
參考: me
2011-10-13 3:56 pm
the first answer is wrong
收錄日期: 2021-04-13 18:17:37
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