Question

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

Answer 1

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

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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

$\begin{gathered}a = \frac{4}{2} \\ \\ a = 2\end{gathered}$