Question

1.
If the polynomial x3 – 6x2 + ax + 3 leaves a remainder 7 when divided by (x - 1), then the
value of 'a' is
a) 7
b) 9
c) 0
d) 8
​

Answer 1

Answer:

f(x)=x  

3

+ax  

2

+bx+6

(x−2) in a factor ⇒f(2)=0

f(2)⇒2  

3

+a(2)  

2

+2b+6=0

⇒8+4a+2b+b=0

⇒4a+2b+14=0

⇒2a+b+7=0 -(1)

f(x−3)=3 (Remainder)

⇒f(3)⇒3  

3

+a(3)  

2

+b×3+6=3

⇒27+9a+3b+b=3

⇒9a+3b+30=0

⇒3a+b+10=0 _____ (2)

From (1) & (2)

b=−2a−7 & b=−10−3a

−2a−7=−10−3a

3a−2a=−10+7

a=−3

from (3)

b=−2(a)−7=2(−3)−7

  =6−7

b=−1

Step-by-step explanation:

Answer 2

Answer:

so, the answer is b) 9

Step-by-step explanation:

p(x) = x - 1

x - 1 = 0

→x = 0 + 1

= 1

x³ - 6x² + ax + 3

→ (1)³ - 6(1)² + a(1) + 3 = 0

→ 1 - 6×1 + a + 3 = 0

→1 - 6 + a + 3 = 0

→ -5 + a + 3 = 0

→ -5 + 3 + a = 0

→ -2 + a = 0

→ a = 0 + 2

→ a = 2 + 7 [because it leaves a reminder 7 ]

= 9

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