if one root of the quadratic equation kx^2-5x+2=0 is 4 times the other find k?
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Answered by
22
Answer:
k = 2
Step-by-step explanation:
Let the roots of the equation be A and B respectively.
Given: A = 4B
If the equation can be represented as the following
ax^2 + bx + c =0
where a = k
b= -5 & c=2
the sum of the roots is given by -b/a
which is 5/k= A + B=> 5/k = 5B .......(1)
Also, product of roots = c/a
2/k= A(B) => 2/k = 4B^2......(2)
From equation (1) we get k = 1/B
Putting value of k in equation (2), we get
2B = 4B^2
B = 1/2
Hence k =2
Hope this helps you...
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Just for cross checking the roots of the equation come out to be 1 and 4
which is the condition of the question...
Answered by
0
Answer:
k=2 is the answer of this question
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