1) Examine whether y+3 is a …
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Sankhadip Bag 6 years, 10 months ago
1) Yes, y+3 is a factor of f(x)= 2y3 + 3y2 - 7y + 6
2) Since (x-1) is a factor of f(x)= 4x3 + 3x2 - 4x +k , x= 1 is a root of f(x). Therefore,
f(1)= 4*(1)3 + 3*(1)2 - 4(1) +k = 0
or, 4*1 +3*1 - 4 + k = 0
or, 4 + 3 - 4 + k = 0
or, 3 + k = 0
or, k = -3
Therefore, value of k is -3
3) x3 + y3
= (x+y)3 - 3xy(x+y) [ since x3 + y3 = (x + y)3 - 3xy(x+y)]
= (5)3 - 3 * (6) * (5) [ x+y = 5 and xy = 6 given]
= 125 - 90
= 35
Therefore, the value of x3 + y3 is 35
0Thank You