A quandratic equation whose difference of roots is 3 and sum of squares is 29 is given by;
(a).xsquare -7x+10=0
(b).xsquare +9x+14=0
(c).xsquare +7x+10=0
(d).xsquare -7x-10=0
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let roots be u and v. let u > v.
u - v = 3 and u² + v² = 29
2 u v = u² + v² - (u - v)² = 29 - 9 =20
=> (u + v)² = u² + v² + 2 u v = 29 + 20 = 49
u + v = 7 or -7
equations are: x² - (u+v) x + u v = 0
x² - 7 x + 10 =0
x² + 7 x + 10 = 0
u - v = 3 and u² + v² = 29
2 u v = u² + v² - (u - v)² = 29 - 9 =20
=> (u + v)² = u² + v² + 2 u v = 29 + 20 = 49
u + v = 7 or -7
equations are: x² - (u+v) x + u v = 0
x² - 7 x + 10 =0
x² + 7 x + 10 = 0
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