If the difference of the roots of Quadratic equation is 4 and the difference of their cube is 243 find the Quadratic equation
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Step-by-step explanation:
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Step-by-step explanation:
let the roots be m , n
m³ - n³ = 243
m - n = 4
m² + mn + n² = 243/4
(n+4)² + n(n+4) + n² = 243/4 = 60.75
3n² + 12n + 16 = 60.75
3n² + 12n + 16 = 60.75
3n² + 12n - 43.25 = 0
n = (- 12 ± √ 144 + 519)/6 = - 2 ± √663/6
n = - 2 ± √663/6
m = 2 ± √663/6
there are two equations
1st. case
m + n = √663/3
mn = 663/6 - 4 = 639/6 = 213/2
the Quadratic equation is
x² - √663x/3 + 213/2 = 0
2nd. case
m + n = -√663/3
mn = 663/6 - 4 = 639/6 = 213/2
the Quadratic equation is
x² + √663x/3 + 213/2 = 0
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General Form of the equation is :
x² ± √663x/3 + 213/2 = 0
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