UPSC Exam > UPSC Questions > Solve 👇👇 Given that function h(x)=x²-7x+6 (...
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Given that function h(x)=x²-7x+6
(1) express h(a²)-h(a) in terms of a
(2)find the value of k for which h(k) =0,
(3) express h(2a)-h(a+1)in terms of a.?
Given that function h(x)=x²-7x+6
(1) express h(a²)-h(a) in terms of a
(2)find the value of k for which h(k) =0,
(3) express h(2a)-h(a+1)in terms of a.?
Most Upvoted Answer
Solve 👇👇 Given that function h(x)=x²-7x+6 (1) express h(a²)-h(a) in ...
Expressing h(a²) - h(a) in terms of a:
To express h(a²) - h(a) in terms of a, we first need to find h(a²) and h(a) separately.
1. h(a²) = (a²)² - 7(a²) + 6 = a⁴ - 7a² + 6
2. h(a) = a² - 7a + 6
Now, h(a²) - h(a) = (a⁴ - 7a² + 6) - (a² - 7a + 6)
= a⁴ - 7a² + 6 - a² + 7a - 6
= a⁴ - 8a² + 7a
Finding the value of k for which h(k) = 0:
To find the value of k for which h(k) = 0, we set h(k) = k² - 7k + 6 = 0
This can be factored as (k - 1)(k - 6) = 0
Therefore, k = 1 or k = 6
Expressing h(2a) - h(a + 1) in terms of a:
To express h(2a) - h(a + 1) in terms of a, we first need to find h(2a) and h(a + 1) separately.
1. h(2a) = (2a)² - 7(2a) + 6 = 4a² - 14a + 6
2. h(a + 1) = (a + 1)² - 7(a + 1) + 6 = a² + 2a + 1 - 7a - 7 + 6 = a² - 5a
Now, h(2a) - h(a + 1) = (4a² - 14a + 6) - (a² - 5a)
= 4a² - 14a + 6 - a² + 5a
= 3a² - 9a + 6
To express h(a²) - h(a) in terms of a, we first need to find h(a²) and h(a) separately.
1. h(a²) = (a²)² - 7(a²) + 6 = a⁴ - 7a² + 6
2. h(a) = a² - 7a + 6
Now, h(a²) - h(a) = (a⁴ - 7a² + 6) - (a² - 7a + 6)
= a⁴ - 7a² + 6 - a² + 7a - 6
= a⁴ - 8a² + 7a
Finding the value of k for which h(k) = 0:
To find the value of k for which h(k) = 0, we set h(k) = k² - 7k + 6 = 0
This can be factored as (k - 1)(k - 6) = 0
Therefore, k = 1 or k = 6
Expressing h(2a) - h(a + 1) in terms of a:
To express h(2a) - h(a + 1) in terms of a, we first need to find h(2a) and h(a + 1) separately.
1. h(2a) = (2a)² - 7(2a) + 6 = 4a² - 14a + 6
2. h(a + 1) = (a + 1)² - 7(a + 1) + 6 = a² + 2a + 1 - 7a - 7 + 6 = a² - 5a
Now, h(2a) - h(a + 1) = (4a² - 14a + 6) - (a² - 5a)
= 4a² - 14a + 6 - a² + 5a
= 3a² - 9a + 6
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Solve 👇👇 Given that function h(x)=x²-7x+6 (1) express h(a²)-h(a) in terms of a (2)find the value of k for which h(k) =0,(3) express h(2a)-h(a+1)in terms of a.?
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