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1) Examine whether y+3 is a …

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1) Examine whether y+3 is a factor of polynomial 2y³ + 3y² - 7y + 6

2) Find the valude of k, if (x-1) is a factor of 4x³ + 3 x 2 - 4 x + k

3) If x + y = 5 and xy = 6, then find x³+ y³

Posted by Madhav V 8 years, 5 months ago

CBSE > Class 09 > Mathematics

1 answers

Sankhadip Bag 8 years, 5 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 + y³is 35

0Thank You

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