Question

If x=0 and x=2 are zeroes of P(x)= 2x3 -5x2 +ax+b ,find the values of a and b . need step by step solution

Answer 1

put x=0 in the polynomial
$p(0) = 2( {0)}^{3} - 5( {0)}^{2} + a(0) + b = 0 \\0 - 0 + 0 + b = 0 \\ b = 0 \\ put \: x = 2 \\ p(2) = 0 \\ 2( {2)}^{3} - 5( {2)}^{2} + a(2) + b = 0 \\ 16 - 20 + 2a + b = 0 \\ - 4 + 2a + 0 = 0 \\ 2a = 4 \\ a = \frac{4}{2} \\ a = 2$