F4 Nature of roots

2011-10-13 4:03 pm

if a and b are the roots of the quadratic equation x^2-3kx+18=0 and a=2b, find the possible value(s) of k.

If one root of quadratic equation -2x^2+3(p-1)x-10=0 is less than the other root by 4, find the possible value(s) of p.

回答 (1)

螞蟻雄兵

2011-10-13 5:28 pm

✔ 最佳答案

if a and b are the roots of the quadraticequation x^2－3kx+18=0 anda=2b，
find the possible value(s) of k.
Sol
a+b=3k，ab=18
2b^2=18
b=+/-3
(1) b=3
a=6
6+3=3k
k=3
(2) b=－3
a=-6
－6－3=3k
k=－3
綜合(1)(2)
k=+/-3

If one root of quadratic equation -2x^2+3(p－1)x-10=0 is less than the other root
by 4， find thepossible value(s) of p.
Sol
設兩根為a，b，且a－b=4
a+b=3(p－1)/2，ab=5
a－b=4
a=b+4
b(b+4)=5
b^2+4b－5=0
(b－1)(b+5)=0
b=1 or b=－5
(1) b=1
a=5
5+1=3(p－1)/2
p=5
(2) b=－5
a=－1
－1－5=3(p－1)/2
p=－3
綜合(1)(2)
p=5or －3

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