Find the values of m and n if 1 and -4 are the roots of the equation mx^2+nx-4=0.?

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answers:
llaffer say: If 1 and -4 are roots, then the factors are (x - 1) and (x + 4)

So if we multiply them together and set it equal to 0, we can expand it to get the polynomial that gets us those roots:

(x - 1)(x + 4) = 0
x² + 3x - 4 = 0

We can multiply both sides of the equation by a constant and it won't change the roots, but since our constant term is -4 and matches what you are looking for, we don't have to. Now looking at the coefficients we see that:

m = 1 and n = 3
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khalil say: x = 1 → m + n - 4 = 0

x = -4 → 16m - 4n - 4 = 0

make the coefficients m or n equal and opposite sign

i choose m

the first multiplied by (- 16)

-16m - 16n + 64 = 0

16m - 4n - 4 = 0

now add together'

-20n + 60 = 0 → n = 3 ◄◄◄

from the first

m = 4 -n = 4 - 3

m = 1 ◄◄◄
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Iggy Rocko say: (x - 1)(x - -4) = 0
x^2 + 4x - x - 4 = 0
x^2 + 3x - 4 = 0
m = 1, n = 3
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rotchm say: You are told that :

m*(1)² + n*(1) - 4 = 0 and that
m*(-4)² + n*(-4) - 4 = 0.

Just solve for m & n as you learned many months ago.
Done!
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llaffer say: If 1 and -4 are roots, then the factors are (x - 1) and (x + 4)

So if we multiply them together and set it equal to 0, we can expand it to get the polynomial that gets us those roots:

(x - 1)(x + 4) = 0
x² + 3x - 4 = 0

We can multiply both sides of the equation by a constant and it won't change the roots, but since our constant term is -4 and matches what you are looking for, we don't have to. Now looking at the coefficients we see that:

m = 1 and n = 3
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mizoo say: ax^2 + bx + c = 0
Sum of root: -b/a
Product of roots: c/a

mx^2+ nx - 4 = 0:
S: 1 + (-4) = -n/m
P: 1 * (-4) = -4/m

m = 1
n = 3
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