Question

If 2 and 0 are the zeros of the polynomial f(x) =
$2 {x}^{3} - 5 {x}^{2} + ax + b$
find the values of a and b.​

Answer 1

Here 2 & 0 are the zeros of given below equation ,

$2 {x}^{3} - 5 {x}^{2} + ax + b \\ \\ so \: put \: the \: zeroes \: in \: this \: equation \: 2 \: and \: 0 \: respectively \\ \\ first \: put \: 2 \\ \\ 2 ({2})^{3} - 5 ({2})^{2} + a(2) + b = 0 \\ \\ 2(8) - 5(4) + 2a + b = 0 \\ \\ 16 - 20 + 2a + b = 0 \\ \\ 2a + b = 4 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: .................(1) \\ \\ now \: put \: 0 \\ \\ 2 ({0})^{3} - 5 ({0})^{2} + a(0) + b = 0 \\ \\ (0) - (0) + (0) + b = 0 \\ \\ b = 0 \\ \\ now \: put \: the \: value \: of \: \: \: \: \: b \: \: \: \: in \: the \: equation \: (1) \: we \: get \: \\ \\ 2a + (0) = 4 \\ \\ 2a = 4 \\ \\ a = 2$

Hope it helps.....

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