Question

f(x) = 2x cube - 5 x square + ax + b zeroes are 2 and 0 . Find a and b.

Answer 1

$Heya$‼

$Given\:polynomial ,$
$f (x) = 2x^3-5x^2+ax+b$

Also the given zeroes are 2 and 0 .

So, $f (2) = 2(2)^3-5(2)^2+a(2)+b$

$=> 2(8)-5(4)+2a+b=0$

$=> 16-20+2a+b=0$

$=>-4+2a+b=0$ ...{1}


And, $f (0) = 2(0)^3-5(0)^2+a(0)+b$

$=> 2(0)-5(0)+0+b=0$

$=> 0-0+0+b=0$

$=> b=0$ ...{2}


Substituting the value of b in {1} :

$-4 + 2a + 0 = 0$

$2a=4$

$a=\frac{4}{2}$

$a=2$


Hence, the values of a and b are 2 and 0 respectively.