Question

If x=0and x=2 are zeroes of p(x)=2x^3-5x^2+ax+b find the values of a and b

Answer 1

Hey there!

$p(x) = 2x {}^{3} - 5x {}^{2} + ax + b$

$x = 0$

$p(0) = 2(0) {}^{3} - 5 (0){}^{2} + a \times 0 + b$

$0 - 0 + 0 + b = 0$

$0 - 0 + b = 0$

$- 0 + b = 0$

$b = 0$

$p(2) = 2 \times (2) {}^{3} - 5 \times 2 {}^{2} + a \times 2 + 0 = 0$

$24 - 5 \times 4 + 2a = 0$

$- 4 + 2a = 0$

$2a = 4$

$a = 2$

Hence,
b = 0
a = 2

Hope it helps!!