Question

f(x)=2x3_3x2+ax+b then find the values of a and b​

Answer 1

Answer:

f(x)=x

3

+10x

2

+ax+b

1 and −2 are the zeros of f(x)

Thus,

f(1)=0 and f(−2)=0

f(1)=0

⇒1

3

+10(1)

2

+a(1)+b=0

⇒1+10+a+b=0

⇒a+b+11=0-------------(i)

f(−2)=0

⇒(−2)

3

+10(−2)

2

+a(−2)+b=0

⇒−8+40−2a+b=0

⇒−2a+b+32=0 ---------------(ii)

Substracting (ii) and (i), we get

⇒a+b+11−(−2a+b+32)=0

⇒a+b+11+2a−b−32=0

⇒3a−21=0

⇒a=7

Putting this value in (i), we get

⇒7+b+11=0

⇒b+18=0

⇒b=−18

Thus,

a=7 and b=−18

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