It is given that the equation 16x 2 − 24x + 10 = k, where k is a constant, has exactly one root. Find the value of this root.
Answers
Answer:
12334567891012345678
Given : equation 16x² − 24x + 10 = k,
has exactly one root
To Find : Value of the root
Solution:
16x² − 24x + 10 = k
has exactly one root
hence y = k must be a tangent
f(x)= 16x² − 24x + 10
f'(x)= 32x - 24
32x - 24 = 0
=> x = 24/32
=>x = 3/4
root is 3/4
16(3/4)² − 24(3/4) + 10 = k
=> 9 - 18 + 10 = k
=> k = 1
Another method:
16x² − 24x + 10 = k
=> (4x)² - 2*3*4x + 3² + 1 = k
=> (4x - 3)² = k - 1
4x - 3 = | k - 1|
As has exactly one root.
so | k - 1| = 0
=> k = 1
4x - 3 = 0
=> x = 3/4
Hence root is 3/4
one more method
16x² − 24x + 10 = k
=> 16x² − 24x + 10 - k = 0
Exactly one root hence D=0
=> (-24)² - 4(16)(10 - k) = 0
=> 9 - 10 + k = 0
=> k = 1
16x² − 24x + 10 = 1
=> 16x² − 24x + 9 = 0
=> (4x - 3)² = 0
=> x = 3/4
Learn More:
Find k, if one root of the equation 5x2 + 6x + k = 0is five times the other.
brainly.in/question/13872549
If one root of the equation x2+ 7x+ p = 0 be reciprocal of the other ...
brainly.in/question/13304461