It is given that k is a root of the quadratic equation x^2+x+c=0.
a.)Express c in term of k.
b.)Find the other root of the equation in (a)
f.4.Quadratic Equations~help
2010-09-21 4:23 am
回答 (2)
2010-09-21 4:33 am
✔ 最佳答案
a)k^2 + k + c = 0c = - k^2 - kc = - k(k + 1)b) Method 1 :Product of the roots = c/1 = c ,The other root * k = cThe other root * k = - k(k + 1)The other root = - k - 1Method 2 :Sum of the roots = - 1The other root + k = - 1The other root = - k - 1
2010-09-21 4:53 am
a) x^2 + x + c = 0
k is a root of the equation.
k^2 + k + c = 0
c = -k-k^2
b) By quadratic formula,
x = [-1 ± √(1 - 4c)]/2
= [-1 ± √(1 - 4(-k^2-k))]/2
= [-1 ± √(4k^2 + 4k + 1)] / 2
= [-1 ± (2k+1)] /2
= (-1+2k+1)/2 or (-1-2k-1)/2
= k or -k-1
Hence the other root is -k-1
k is a root of the equation.
k^2 + k + c = 0
c = -k-k^2
b) By quadratic formula,
x = [-1 ± √(1 - 4c)]/2
= [-1 ± √(1 - 4(-k^2-k))]/2
= [-1 ± √(4k^2 + 4k + 1)] / 2
= [-1 ± (2k+1)] /2
= (-1+2k+1)/2 or (-1-2k-1)/2
= k or -k-1
Hence the other root is -k-1
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