Question

Pls slove this
If 2 and 0 are the zeros of the polynomial f (x)= 2x^3 - 5x^2 +ax+b then find the values of a and b

Answer 1

Heya !!!

here is your answer !!!

given that :-. zeroes of polynomial =>

2 and 0

now ,

on putting the value of zeroes. in polynomial we get

2x³ - 5x² + ax + b.

p ( 2 )

=> 2 ( 2) ³ - 5 ( 2 )² + 2a + b = 0

=> 2 * 8 - 5 * 4 + 2a + b. = 0

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

=> -4 + 2a + b = 0

=> 2a + b = 4. ----------------(1) .

now , on putting 0 in polynomial we get

=>
2x³ - 5x² + ax + b. = 0

2 (0)³ - 5 ( 0 ) ² + a* 0 + b =0

=> b = 0 --------------(2)

on putting the value of 2 in equation 1 we get

=> 2a + b = 4

=> 2a +0 = 4

a = 2


hence the value of a = 2

and the value of b = 0
hope it helps you dear !!!





thanks !!

ranjankumar

☺☺

Answer 2

Given Equation is f(x) = 2x^3 - 5x^2 + ax + b.

Given that 2 and 0 are the zeroes of the polynomial.

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

       = 16 - 20 + 2a + b

       = -4 + 2a + b.



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

       = b.



On solving both equations, we get

-4 + 2a + b = b

-4 + 2a = 0

2a = 4

a = 2



Substitute a = 2 in (1), we get

-4 + 2a + b = 0

-4 + 2(2) + b = 0

-4 + 4 + b = 0

b = 0



Therefore the value of a = 2 and b = 0.



Hope this helps!