Find the values of a and b so that (2x³ + ax² +x+b) has (x + 2) and
(2x - 1) as factors.
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Step-by-step explanation:
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mutturevula8840
3 days ago
Math
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Find the value of a and b so that (2x³+ax²+x+b) has (x+2) and (2x-1) as a factors.
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sandhuaman1234567
sandhuaman1234567 Ambitious
Answer:
the value of A=5 and the value of B=2
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vanshkjain000 Ambitious
Answer:
a = 5, b = -2
Step-by-step explanation:
(x+2) and (2 x-1) is factor of 2 x³+ a x²+ x + b
(x+2) = 0
x = -2
And,
(2 x-1) = 0
2 x = 1
X = 1/2
P(X) = 0
P(-2) = 0
2 × (-2)³ + a × (-2)² + (-2) + b = 0
2 × -8 + a × 4 - 2 + b = 0
-16 + 4 a - 2 + b = 0
4 a + b = 18 ---------(1)
Also X = 1/2
P(X) = 0
P(1/2) = 0
2 × (1/2)³ + a × (1/2)² + 1/2 + b = 0
2 × 1/8 + a × 1/4 + 1/2 + b = 0
1/4 + a/4 + 1/2 + b = 0
1 + a + 2 + 4 b /4 = 0
a + 4 b + 3 = 0
a + 4 b = -3 -----------(2)
From equation (1) and (2) we get,
(4 a + b = 18) × 1
(a + 4 b = -3) × 4
4 a + b = 18
4 a + 16 b = -12
Subtracting (2) from (1),
-15 b = 30
∴ b = -2
Putting value of b in (1),
4 a + (-2) = 18
∴ a = 5