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2020-10-06 4:55 pm
3. The quadratic equation 𝑥^2+(𝑚+3)𝑥+4𝑚=0 , where 𝑚 is a constant, has equal roots. Find the possible values for 𝑚.
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2020-10-06 5:09 pm
✔ 最佳答案
The quadratic equation x² + (m + 3)x + 4m = 0 has equal roots.Hence, discriminant, Δ = 0
(m + 3)² - 4(1)(4m) = 0
m² + 6m + 9 - 16m = 0
m² - 10m + 9 = 0
(m - 1)(m - 9) = 0
m = 1 or m = 9
2020-10-06 5:12 pm
𝑥^2 +(𝑚+3)𝑥 + 4𝑚 = 0
4m must be a square
factors as (x - 2sqrtm)^2 = 0
root is +/-2sqrtm
expand (x - 2sqrtm)^2
= x^2 - 4 sqrtm + 4m
-4 sqrtm = m+3
m + 4 sqrtm + 3 = 0
use the quad. formula
sqrt m = [-4+/- sqrt(16 - 12)] / 2
sqrt m =[-4 +/- 2]/2
sqrt m = -1 or -3
m = 1 or 9
4m must be a square
factors as (x - 2sqrtm)^2 = 0
root is +/-2sqrtm
expand (x - 2sqrtm)^2
= x^2 - 4 sqrtm + 4m
-4 sqrtm = m+3
m + 4 sqrtm + 3 = 0
use the quad. formula
sqrt m = [-4+/- sqrt(16 - 12)] / 2
sqrt m =[-4 +/- 2]/2
sqrt m = -1 or -3
m = 1 or 9
收錄日期: 2021-04-24 08:01:20
原文連結 [永久失效]:
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