a) Let f(X)=x^2-4kx+5k+6, where k is a real number.Find the discriminant of the equation f(x)=0.
b) Hence or otherwise, find the range of values of k so that f(x) >=0 for all real values of x.
a maths question
2007-12-09 5:24 pm
回答 (2)
2007-12-09 5:39 pm
✔ 最佳答案
(a)f(x)=0
x^2-4kx+(5k+6)=0
discriminant =(-4k)^2 -4(5k+6)
=16k^2-20k-24
(b)when f(x) >=0
discriminant<=0
16k^2-20k-24<=0 from a
4k^2-5k-6<=0
(4k+3)(k-2)<=0
-3/4<= k <= 2
2007-12-09 5:48 pm
(a)
f(x)=0
x^2-4kx+(5k+6)=0
discriminant =(-4k)^2 -4(5k+6)
=16k^2-20k-24
(b)when f(x) >=0
discriminant<=0
16k^2-20k-24<=0 from a
4k^2-5k-6<=0
(4k+3)(k-2)<=0
-3/4<= k <= 2
f(x)=0
x^2-4kx+(5k+6)=0
discriminant =(-4k)^2 -4(5k+6)
=16k^2-20k-24
(b)when f(x) >=0
discriminant<=0
16k^2-20k-24<=0 from a
4k^2-5k-6<=0
(4k+3)(k-2)<=0
-3/4<= k <= 2
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