Would we use the b^2-4ac method? I'm confused :/
help is much appreciated :)
help is much appreciated :)
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This is true only when the quadratic equation is a perfect square. or x has only one root.
If we assume the quadratic equation has one root, then B*B - 4*A*C = 0
Therefore
(m+4)^2 - 4 * 1 * (4m+1) = 0
by expanding and rearranging yo get
m ^ 2 - 8m + 12 = 0
If we assume the quadratic equation has one root, then B*B - 4*A*C = 0
Therefore
(m+4)^2 - 4 * 1 * (4m+1) = 0
by expanding and rearranging yo get
m ^ 2 - 8m + 12 = 0
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You haven't written the entire question. I suppose it must be
"The quadratic equation x^2+(m+4)x+(4m+1)=0 [has a single real root.] Show that m^2 - 8m + 12 = 0."
A quadratic equation has a single real root if and only if the discriminant is 0. The discriminant is b^2 - 4ac for a general quadratic, which here is...
(m+4)^2 - 4(1)(4m+1)
= m^2 + 8m + 16 - 16m - 4
= m^2 - 8m + 12
which must be 0 as noted.
(Edit: fixed minor typo.)
"The quadratic equation x^2+(m+4)x+(4m+1)=0 [has a single real root.] Show that m^2 - 8m + 12 = 0."
A quadratic equation has a single real root if and only if the discriminant is 0. The discriminant is b^2 - 4ac for a general quadratic, which here is...
(m+4)^2 - 4(1)(4m+1)
= m^2 + 8m + 16 - 16m - 4
= m^2 - 8m + 12
which must be 0 as noted.
(Edit: fixed minor typo.)
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b^2-4ac=D (m+4)^2-4(4m+1)=m^2+8m+16-16m-4=m^2-8m+1…