Question

Solve the equation 2x^3-5x^2+x+2=0 given that 2 is a zero of f(x)= 2x^3-5x^2+x+2

Answer 1

The polynomial equation $2x^{3} - 5 x^{2} + x + 2 = 0$ given that 2 is zero of

f(x) = $2x^{3} - 5 x^{2} + x +2$

According to the question,

f(x)  $=2x^{3} - 5 x^{2} + x + 2$

$f(2)= 2(2)^{3} - 5 (2)^{2} + 2 + 2 \\= 2(8) - 5(4) +4\\= 16 - 20 + 4\\= -4 + 4\\= 0.$

Hence, the polynomial equation $2x^{3} - 5 x^{2} + x + 2 = 0$ given that 2 is zero of f(x)  $=2x^{3} - 5 x^{2} + x + 2$.

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