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31 Jul 2021, 05:25
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If the function g(x) is defined by the equation \(g(x) = ax^2– 3x – b\), where a and b are constants, g(5) = 0, and g(–2) = 0, then ab =
A. –10
B. 10
C. 15
D. 100
E. It cannot be determined from the information given.
A. –10
B. 10
C. 15
D. 100
E. It cannot be determined from the information given.
31 Jul 2021, 06:09
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taha1234
Pretty straightforward: Substitute x as 5 and then -2 to get two linear equations in a and b. Two variables and two linear equations will give you the value of variables.
(1) g(5)=0
\(g(x) = ax^2– 3x – b\)
\(g(5) = a5^2– 3*5– b=0…………b=25a-15\)
(2) g(-2)=0
\(g(x) = ax^2– 3x – b\)
\(g(5) = a(-2)^2– 3*(-2)– b=0…………b=4a+6\)
From 1 and 2, we get 25a-15=4a+6………21a=21……a=1
b=4*1+6=10
ab=1*10=10
B
15 Dec 2021, 10:51
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Given that \(g(x) = ax^2– 3x – b\) and g(5) = 0, and g(–2) = 0 and we need to find the value of ab
Let's start with g(5).
To find value of g(5) we need to substitute x=5 in \(g(x) = ax^2– 3x – b\)
=> \(g(5) = a*5^2– 3*5 – b\) = 25a - 15 - b = 0 (given)
=> 25a - b = 15 .... (1)
Similarly, let's find the value of g(-2)
To find value of g(-2) we need to substitute x=-2 in \(g(x) = ax^2– 3x – b\)
=> \(g(-2) = a*(-2)^2– 3*(-2) – b\) = 4a +6 - b = 0 (given)
=> 4a - b = -6 .... (2)
(1) - (2) we get
25a - b - (4a - b) = 15 - (-6)
=> 25a - b - 4a + b = 15 + 6 = 21
=> 21a = 21
=> a = 1
Putting a = 1 in (1) we get
25 *1 - b = 15
=> b = 25 - 15 = 10
=> a*b = 1*10 = 10
So, Answer will be B
Hope it helps!
Watch the following video to learn the Basics of Functions and Custom Characters
Let's start with g(5).
To find value of g(5) we need to substitute x=5 in \(g(x) = ax^2– 3x – b\)
=> \(g(5) = a*5^2– 3*5 – b\) = 25a - 15 - b = 0 (given)
=> 25a - b = 15 .... (1)
Similarly, let's find the value of g(-2)
To find value of g(-2) we need to substitute x=-2 in \(g(x) = ax^2– 3x – b\)
=> \(g(-2) = a*(-2)^2– 3*(-2) – b\) = 4a +6 - b = 0 (given)
=> 4a - b = -6 .... (2)
(1) - (2) we get
25a - b - (4a - b) = 15 - (-6)
=> 25a - b - 4a + b = 15 + 6 = 21
=> 21a = 21
=> a = 1
Putting a = 1 in (1) we get
25 *1 - b = 15
=> b = 25 - 15 = 10
=> a*b = 1*10 = 10
So, Answer will be B
Hope it helps!
Watch the following video to learn the Basics of Functions and Custom Characters
