a) If (1-2k)x^2 + 8kx - (2+8k) = 0 has equal roots, find the value of k.
x^2 - 2kx^2 + 8kx - 2 - 8k = 0 <==== what do i do next???
b) If x^2 + kx + 2x + 2k = 0 has real and equal roots, find the value of k.
c) Find the value of p if the quadratic equation 3x^2 - 1 = 6x - 2p has real and equal roots.
*How do i which is a, b and c? please only answer if you don't mind to show me the steps.
P.S. - Please don't waste your time answering this question if you are just going to troll and say something which does not answer the question because you are just wasting your time and mine.
x^2 - 2kx^2 + 8kx - 2 - 8k = 0 <==== what do i do next???
b) If x^2 + kx + 2x + 2k = 0 has real and equal roots, find the value of k.
c) Find the value of p if the quadratic equation 3x^2 - 1 = 6x - 2p has real and equal roots.
*How do i which is a, b and c? please only answer if you don't mind to show me the steps.
P.S. - Please don't waste your time answering this question if you are just going to troll and say something which does not answer the question because you are just wasting your time and mine.
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Hello.
When you have a quadratic equation
ax² + bx + c = 0
you have to calculate the discriminant:
∆ = b² - 4ac.
If this discriminant is nil, the quadratic equation is a perfect square with only one value as double root.
So when you want a double root, all you have to do is to find the value that make the discriminant equal to zero.
a) = = = = = = = = = = = =
(1 - 2k)x² + 8kx - (2 + 8k) = 0
If this equation has a double root, then its discriminant is nil:
∆ = (8k)² + 4(1 - 2k)(2 + 8k) = 0
64k² + 4(2 + 8k - 4k - 16k²) = 0
64k² + 8 + 16k - 64k² = 0
16k + 8 = 0
k + ½ = 0
k = -½
b) = = = = = = = = = = = =
x² + (k + 2)x + 2k = 0
If this equation has a double root, then its discriminant is nil:
∆ = (k + 2)² - 8k = 0
k² + 4k + 4 - 8k = 0
k² - 4k + 4 = 0
(k - 2)² = 0
k = 2
c) = = = = = = = = = = = =
3x² - 1 = 6x - 2p
3x² - 6x + 2p - 1 = 0
If this equation has a double root, then its discriminant is nil:
∆ = 6² - 12(2p - 1) = 0
36 - 12(2p - 1) = 0
3 - 2p + 1 = 0
p = 2
Elementary,
Dragon.Jade :-)
When you have a quadratic equation
ax² + bx + c = 0
you have to calculate the discriminant:
∆ = b² - 4ac.
If this discriminant is nil, the quadratic equation is a perfect square with only one value as double root.
So when you want a double root, all you have to do is to find the value that make the discriminant equal to zero.
a) = = = = = = = = = = = =
(1 - 2k)x² + 8kx - (2 + 8k) = 0
If this equation has a double root, then its discriminant is nil:
∆ = (8k)² + 4(1 - 2k)(2 + 8k) = 0
64k² + 4(2 + 8k - 4k - 16k²) = 0
64k² + 8 + 16k - 64k² = 0
16k + 8 = 0
k + ½ = 0
k = -½
b) = = = = = = = = = = = =
x² + (k + 2)x + 2k = 0
If this equation has a double root, then its discriminant is nil:
∆ = (k + 2)² - 8k = 0
k² + 4k + 4 - 8k = 0
k² - 4k + 4 = 0
(k - 2)² = 0
k = 2
c) = = = = = = = = = = = =
3x² - 1 = 6x - 2p
3x² - 6x + 2p - 1 = 0
If this equation has a double root, then its discriminant is nil:
∆ = 6² - 12(2p - 1) = 0
36 - 12(2p - 1) = 0
3 - 2p + 1 = 0
p = 2
Elementary,
Dragon.Jade :-)
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The equation ax^2 + bx + c has equal roots when b^2 = 4ac.
a) a = 1-2k; b = 8k and c = -(2+8k)
So 64k^2 = -4(1-2k)(2+8k) = 64k^2 -16k -8 or
16k = -8 or k = -1/2
b) a = 1; b = (k+2) and c = 2k or
(k+2)^2 = 8k or k^2 -4k +4 = 0 or k = 2 will give equal real roots for the given equation.
c) a = 3; b = -6 and c = (2p-1) or
36 = 12(2p-1) then the given equation will have real equal roots
24 p = 48 or p = 2
a) a = 1-2k; b = 8k and c = -(2+8k)
So 64k^2 = -4(1-2k)(2+8k) = 64k^2 -16k -8 or
16k = -8 or k = -1/2
b) a = 1; b = (k+2) and c = 2k or
(k+2)^2 = 8k or k^2 -4k +4 = 0 or k = 2 will give equal real roots for the given equation.
c) a = 3; b = -6 and c = (2p-1) or
36 = 12(2p-1) then the given equation will have real equal roots
24 p = 48 or p = 2