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Find a polynomial `p(x)` of degree 4, which has `x^2-3x+2` as a factor and also given that `p(-1)=24,p(-2)=132` and ` p(0)=2`. |
Answer» `p(x)=(x^2-3x+2)(ax^2+bx+c)` put x=0 `P(0)=2c=2` `c=1` put x=-1 `p(-1)=(1+3+2)(a-b+1)=24` `6(a-b+1)=24` `a-b=3-(1)` put x=-2 `p(-2)=(4+6+2)(4a-2b+1)=132` `12(4a-2b+1)=132` `2a-b=5-(2)` subtracting equation 1 from equation 2 `a=2` `b=-1` `P(x)=(x^2-3x+2)(ax^2+bx+c)` `P(x)=(x^2-3x+2)(2x^2-x+1)`. |
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