If 4 is one of the roots for quadratic equation 2kx2-4kx+10k=0 then find k.
Answers
Given :- if 4 is one of the roots for quadratic equation 2kx² - 4kx + 10k = 0 then find k. ?
Solution :-
→ 2kx² - 4kx + 10k = 0
→ 2k(x² - 2x + 5) = 0
→ 2k = 0 , or x² - 2x + 5 = 0
as we can see , if 2k = 0, => k = 0, then the whole equation becomes 0 . in this case quadratic equation is not possible.
now,
→ if x² - 2x + 5 = 0
we know that, If A•x² + B•x + C = 0 ,is any quadratic equation,
then its discriminant is given by;
- D = B² - 4•A•C
• If D = 0 , then the given quadratic equation has real and equal roots.
• If D > 0 , then the given quadratic equation has real and distinct roots.
• If D < 0 , then the given quadratic equation has unreal (imaginary) roots...
comparing x² - 2x + 5 = 0 with A•x² + B•x + C = 0 we get,
- A = 1
- B = (-2)
- C = 5
So,
→ D = B² - 4AC
→ D = (-2)² - 4 * 1 * 5
→ D = 4 - 20
→ D = (-16)
→ (-16) < 0
→ D < 0 .
therefore, the given quadratic equation has unreal (imaginary) roots .
Hence, we can conclude that their is no such value of k for which 4 is the roots of the given quadratic equation.
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Given : 4 is one of the roots for quadratic equation 2kx² - 4kx + 10k = 0
To Find : Value of k
Solution:
2kx² - 4kx + 10k = 0
=> 2k(x² - 2x + 5) = 0
=> k = 0 or x² - 2x + 5 = 0
k ≠ 0 as if k = 0 then its no more Quadratic Equation
for all other values of K
x² - 2x + 5 = 0
(-2)² - 4(1)(5) = -16 < 0
Hence no real roots
Hence 4 can not be a root of the Equation
Hence Question data is wrong
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