Question

if y=2 and y=0 are the zeroes of the polynomial f(y)=2y³-5y²+ay+b find the values of a and b

Answer 1

if y =2
2(8)-5(4)+2a+b=0
16-20+2a+b=0
2a+b=4 equation 1
if y=0
0-0+0+b=0
so b=0
put b in equation 1
2a+0=4
2a=4
a=2
so a=2,b=0

Answer 2

Given,

y=2 and y=0 are the zeroes of the polynomial f(y)=2y³-5y²+ay+b=0

To find,

The values of a and b.

Solution,

Since y=2 and y=0 are zeroes of the polynomial, therefore f(2) = 0 and     f(0) = 0.

And with this, we can equate values of a and b.

Now,

⇒   f(y) = 2y³-5y²+ay+b=0

⇒   f(2) = 2(2)³-5(2)²+2a+b=0

⇒   f(2) = 2(8)-5(4)+ 2a+b=0

⇒   f(2) = 16 - 20 + 2a + b =0.

⇒   2a + b - 4 = 0.

Similarly,

⇒   f(0) = 2(0)³-5(0) +0a +b = 0

⇒   f(0) =  b = 0.

Therefore, the value of b = 0.

Put b = 0 in equation, 2a+b =4.

⇒   2a + b = 4

⇒   2a = 4

⇒   a =2

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

a = 2 and b = 0.