Question

If 2 and 0 are zeros of the polynomials f(x)=2x cube - 5x square + ax+b then find the value of a and b

Answer 1

Heya !!!


Given that,



2 and 0 are the two zeros of the given Polynomial.




P(X) = 2X³ - 5X² + AX + B




P(2) = 2 × (2)³ - 5 × (2)² + A × 2 + B





=> 2 × 8 - 5 × 4 + 2A + B





=> 16 - 20 + 2A + B = 0





=> 2A + B -4 = 0




=> 2A + B = 4 -------(1)


Also,


X = 0




P(0) = 2 × (0)³ - 5 × (0)² + A × 0 + B





=> 2 × 0 + 5 × 0 + 0 + B





=> B = 0



Putting the Value of B in equation (1)




2A + B = 4




2A + 0 = 4



2A = 4




A = 4/2




A = 2.






HOPE IT WILL HELP YOU....... ;-)

Answer 2

Given that 2 and 0 are two zeroes,

Then, x = 2 and x = 0

×××××××××××××

Putting the value(s) one by one in the given equation,

Taking, x = 2

2x³ - 5x² + ax + b = 0

2(2)³ - 5(2)² + a(2) + b = 0

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

16 - 20 + 2a + b = 0

-4 + 2a + b = 0

2a + b = 4 -------1equation

=====================

Taking, x = 0

2x³ - 5x² + ax + b = 0

2(0)³ - 5(0)² + a(0) + b = 0

b = 0

Then, putting the value of b in 1equation,

2a + b = 4

2a + 0 = 4

2a = 4

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




I hope this will help you


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