Question

If ( x-2 ) and (x +3) are factors of x3 + ax2 +bx -30, find a and b.​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

$\Large a=6 \ and \ b=-1$

Step-by-step explanation:

$\Large \text{ Given p(x)= x^3 + ax^2 +bx -30 and two zeroes (x-2) and (x+3) }\\\\\\\Large \text{we have to find value of a and b}\\\\\\\Large \text{putting zeroes values in p(x)}\\\\\\\Large x-2=0 \ so \ x=2 \ and \ x+3=0 \ so \ x=-3\\\\\\\Large \text{putting x=2 in p(x) we get}\\\\\\\Large p(2)=2^3+2^2a+2b-30=0\\\\\\\Large 4a+2b=22\\\\\\\Large b=11-2a \ ...(i)$

$\Large \text{Now put x=-3 in p(x)}\\\\\\\Large p(-3)=(-3)^3+9a-3b-30=0\\\\\\\Large 9a-3b=57\\\\\\\Large b=3a-19 \ ....(ii)\\\\\\\Large \text{From (i) and (ii) we have}\\\\\\\Large 11-4a=3a-19\\\\\\\Large 30=5a\\\\\\\Large a=6\\\\\\\Large \text{putting a=6 in (i)}$

$\Large b=11-2a\\\\\\\Large b=11-2\times6\\\\\\\Large b=11-12\\\\\\\Large \text{b = - 1}\\\\\\\Large \text{Thus we get a=6 \ and \ b=-1 }$