f.4,,amathz
2008-09-27 11:29 pm
If the roots of the equation x^2+2x-7=0 are 2a+3 and 2b+3, find the quadratic equation with roots a^2 and b^2.
回答 (2)
2008-09-27 11:45 pm
2008-09-27 11:55 pm
If the roots of the equation x2+2x-7=0 are 2a+3 and 2b+3, find the quadratic equation with roots a2 and b2
From the root-coefficient relationship,
if the roots of ax2 + bx + c are α and β，
α + β = - b / a
αβ = c / a
Therefore,
If the roots of the new equation are a2 and b2,
α + β = a2 + b2
αβ = a2b2
Therefore, the new equation is x2 - (a2 + b2)x + a2b2
From the root-coefficient relationship,
if the roots of ax2 + bx + c are α and β，
α + β = - b / a
αβ = c / a
Therefore,
If the roots of the new equation are a2 and b2,
α + β = a2 + b2
αβ = a2b2
Therefore, the new equation is x2 - (a2 + b2)x + a2b2
參考: myself
收錄日期: 2021-04-13 16:06:56
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