In the quadratic equation `ax^2 + bx + c = 0`. if `delta = b^2-4ac` and `alpha+beta , alpha^2+beta^2 , alpha^3+beta^3` and `alpha,beta` are the roots

Question

In the quadratic equation `ax^2 + bx + c = 0`. if `delta = b^2-4ac` and `alpha+beta , alpha^2+beta^2 , alpha^3+beta^3` and `alpha,beta` are the roots

In the quadratic equation `ax^2 + bx + c = 0`. if `delta = b^2-4ac` and `alpha+beta , alpha^2+beta^2 , alpha^3+beta^3` and `alpha,beta` are the roots of `ax^2 + bx + c =0`
A. `Delta!=0`
B. `bDelta=0`
C. `cb!=0`
D. `cDelta=0`

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Correct Answer - D
`(alpha^(2)+beta^(2))=(alpha+beta)(alpha^(3)+beta^(3))`
`implies{(alpha+beta)^(2)-2alpha beta}^(2)=(alpha+beta){(alpha+beta)^(2)-2alpha beta(alpha +beta)}`
`=((b^(2))/(a^(2))-(2c)/a)^(2)=(-b/a)((-b^(3))/(a^(3))+(3bc)/(a^(2)))`
`implies((b^(2)-2ac)/(a^(2)))^(2)=((-b)/a)((-b^(3)+3abc)/(a^(3)))`
`implies4a^(2)c^(2)=acb^(2)`
`impliesac(b^(2)-4ac)=0`
As `a!=0`
`impliesc Delta=0`