If (x-2) is a factor of both x2+ax-6 and x2-9x+b,than find the value of a+b.
Answers
Sol: (x - 2) is a factor of x2 + ax - 6 ⇒ (2)2+ a(2) - 6 = 0 ⇒ 2a -2 = 0 ⇒ a = 1 (x - 2) is a factor of x2 - 9x + b ⇒ (2)2 - 9(2) + b = 0 ⇒ b - 14 = 0 ⇒ b = 14 a + b = 1 + 14 = 15.
Answer:
The value of a+b = 15.
Step-by-step explanation:
Factor:
- If (x-p) is the factor of f(x) = x²+ax+b then f(p) = 0
Given mathematical expressions are
x²+ax-6 and x²-9x+b
Let f(x) = x²+ax-6 and g(x) = x²-9x+b
Also given (x-2) is the factor of both f(x) and g(x).
Consider f(x) = x²+ax-6
Since, (x-2) is a factor of f(x) then f(2) = 0
f(2) = 0
(2)²+2a-6 = 0
4+2a-6 = 0
2a-2 = 0
2a = 2
a = 2/2
a = 1
Consider, g(x) = x²-9x+b
Since, (x-2) is a factor of g(x) then g(2) = 0
g(2) = 0
x²-9x+b = 0
(2)²-9(2)+b = 0
4-18+b = 0
-14+b = 0
b = 14
So, the values of a = 1 and b = 14
then a+b = 1+14 = 15
Hence, the value of a+b = 15.
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