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प्रश्न
If x = 0 and x = −1 are the roots of the polynomial f(x) =2x3 − 3x2 + ax + b, find the value of a and b.
उत्तर
The given polynomial is
f(x) =2x3 − 3x2 + ax + b
If x=0 is zeros of the polynomial f(x), then f(0) = 0
`2 xx (0)^3 -3 xx (0)^2 + a xx 0 +b = 0`
`0-0 +0 +b = 0`
`b = 0 ` ....... (1)
Similarly, if x = − 1 is the zeros of the polynomial of f(x),
Then, f (-1) = 0
`2x (-1)^3 - 3 xx (-1)^2 + a xx ( - 1)+ b = 0 `
` - 2 -3-a +b =0 `
` -5-a +b = 0`
Putting the value of b from equation (1)
` -5 -a + 0 =0`
`a= -5`
Thus,
`a=-5`
` b=0`
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