Question: a and b are the roots of the equation 〖10x〗^2-19x-56=0. form a quadratic equation in x whose roots are a+3 and b+3.
Please answer it, thanks.
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2014-10-04 3:00 am
回答 (1)
2014-10-04 7:34 am
✔ 最佳答案
(10x)² - 19x - 56 = 0100x² - 19x - 56 = 0
a and b are the roots.
Sum of the roots: a + b = 19/100
Product of the roots: ab = -56/100
(a + 3) + (b + 3)
= (a + b) + 6
= (19/100) + 6
= 619/100
(a + 3)(b + 3)
= ab + 3a + 3b + 9
= ab + 3(a + b) + 9
= (-56/100) + 3(19/100) + 9
= 901/100
The required quadratic equation :
x² - (619/100)x + (901/100) = 0
100x² - 619x + 901 = 0
參考: micatkie
收錄日期: 2021-04-15 16:47:39
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