(98 POINTS QUESTION LIMITED TIME ONLY!!)
Find the value of a and b so that -1 and -2 are the zeros of the polynomial f(x) = ax³ + 3x²- bx - 6. Also find the third zero.
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Answers
Answer:
f(-1) = -a + 3 + b - 6 = -a+ b -3 =0
b -a = 3
f( -2) = -8a + 12 +2b -6
= -8a + 2b +6 = 0
b -4a = -3
b-a = 3
-5a = 0
a= 0
b= 3
Question:
Find the value of a and b so that -1 and -2 are the zeros of the polynomial f(x) = ax³ + 3x²- bx - 6. Also find the third zero.
Solution:
• If x = -1
=> f(-1) = a(-1)³ + 3(-1)² - b(-1) - 6
=> -a + 3 + b - 6 = 0
=> - a + b - 3 = 0
=> b - a = 3
=> b = 3 + a ______ (eq 1)
• If x = (-2)
=> f(-2) = a(-2)³ + 3(-2)² - b(-2) - 6
=> - 8a + 12 + 2b - 6 = 0
=> - 8a + 2b + 6 = 0
=> - 8a + 2b = - 6
=> - 4a + b = - 3
=> - 4a + (3 + a) = - 3 [From (eq 1)]
=> - 3a + 3 = - 3
=> - 3a = - 6
=> a = 2
Put value of a in (eq 1)
=> b = 3 + 2
=> b = 5
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a = 2 and b = 5
________ [ ANSWER ]
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✡ VERIFICATION :
We have equation according to question :
-a + 3 + b - 6 = -1
From above calculations we have a = 2 and b = 5
Put them in above equation
→ - 2 + 3 + 5 - 6 = -1
→ - 8 + 7 = - 1
→ - 1 = -1
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