Question

0) If x = 2 and x = 0 are zero of polynomial P(x) = 2x
- 5x² + ax + b, then find the value of a and b.

Answer 1

Answer:

a=8

b=0

Step-by-step explanation:

Putting x=2 and x=0 in the polynomial:

$-5(2)^2+2(2)+a(2)+b=-5(0)^2+2(0)+a(0)+b$

$-20+4+2a+b=0+0+0+b$

$-16+2a+b=b$

$-16+2a=0\\2a=16\\a=8$

Now,

$-20+4+2a+b=0\\-16+2(8)+b=0\\-16+16+b=0\\b=0$

Answer 2

Answer:

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

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