數學一問~~

1).If 2-(5開方)is a root of the equation x^2-4x+y=0,find the other root of the equation and
hence find the value of y.
the sum of roots=-(-4)/1=4
2-√5+x=4
x=2+√5
the other root=2+√5
the product of roots=y/1=y=(2+√5)(2-√5)=4-5=-1


2)If one root of 8x^2-ax+9=0 is twice the other,find the roots of the equation and the value of a.
Let the roots be b,2b
b(2b)=9/8
2b^2=9/8
b^2=9/16
b=3/4 or b=-3/4
The roots are (3/4,3/2) or (-3/4,-3/2)
the sum of roots=a/8=3/4+3/2=9/4
a=18 or a=-18

3)The sum of the roots of the equation 12x^2+mx-5=0 exceeds the product of the roots by 11/6.find the value of m. hence solve the equation.
(-m/12)-(-5/12)=11/6
-m+5=22
m=-17
12x^2-17x-5=0
(3x-5)(4x+1)=0
x=5/3 or x=-1/4

4)find the value of k if the product of the roots of the quadratic equation kx^2+4x+k^2-21=0 is 4.
(k^2-21)/k=4
k^2-21=4k
k^2-4k-21=0
(k-7)(k+3)=0
k=7 or k=-3