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If 2x square -(2+k)x +k=0 ,where k is a real no. ,find the roots of the equation.?
Most Upvoted Answer
If 2x square -(2+k)x +k=0 ,where k is a real no. ,find the roots of th...
By comparing the cofficient of given equation
2x²-(2+k)x+k=0
to standard quadratic equation
ax²+bx+c=0
a=2,b=-(2+k),c=k
Discriminant (D)=√b²-4ac
D=(-2-k)²-4×2×k
D=k²+4k+4
D=(k-2)²
by using quadratic formula
first Root=-b+√D/2a
first Root=k/2
second root=-b-√D/2a
=1
2x²-(2+k)x+k=0
to standard quadratic equation
ax²+bx+c=0
a=2,b=-(2+k),c=k
Discriminant (D)=√b²-4ac
D=(-2-k)²-4×2×k
D=k²+4k+4
D=(k-2)²
by using quadratic formula
first Root=-b+√D/2a
first Root=k/2
second root=-b-√D/2a
=1
Community Answer
If 2x square -(2+k)x +k=0 ,where k is a real no. ,find the roots of th...
Solution:
Quadratic Equation:
The given quadratic equation is 2x^2 - (2+k)x + k = 0.
Roots of the Quadratic Equation:
To find the roots of the quadratic equation, we use the formula x = (-b ± √(b^2 - 4ac)) / 2a.
Identifying the Coefficients:
From the given equation, we have a = 2, b = -(2+k), and c = k.
Substitute the Coefficients:
Substitute the values of a, b, and c into the quadratic formula to get x = (-(2+k) ± √((2+k)^2 - 4*2*k)) / 2*2.
Simplify the Expression:
x = (-(2+k) ± √(4 + 4k + k^2 - 8k)) / 4.
x = (-(2+k) ± √(k^2 - 4k + 4)) / 4.
Calculate the Discriminant:
The discriminant, Δ = k^2 - 4k + 4.
Find the Roots:
1. If Δ > 0, then the equation has two distinct real roots.
2. If Δ = 0, then the equation has one real root.
3. If Δ < 0,="" then="" the="" equation="" has="" no="" real="" />
Conclusion:
By following the steps above and analyzing the discriminant, you can determine the nature of the roots of the given quadratic equation.
Quadratic Equation:
The given quadratic equation is 2x^2 - (2+k)x + k = 0.
Roots of the Quadratic Equation:
To find the roots of the quadratic equation, we use the formula x = (-b ± √(b^2 - 4ac)) / 2a.
Identifying the Coefficients:
From the given equation, we have a = 2, b = -(2+k), and c = k.
Substitute the Coefficients:
Substitute the values of a, b, and c into the quadratic formula to get x = (-(2+k) ± √((2+k)^2 - 4*2*k)) / 2*2.
Simplify the Expression:
x = (-(2+k) ± √(4 + 4k + k^2 - 8k)) / 4.
x = (-(2+k) ± √(k^2 - 4k + 4)) / 4.
Calculate the Discriminant:
The discriminant, Δ = k^2 - 4k + 4.
Find the Roots:
1. If Δ > 0, then the equation has two distinct real roots.
2. If Δ = 0, then the equation has one real root.
3. If Δ < 0,="" then="" the="" equation="" has="" no="" real="" />
Conclusion:
By following the steps above and analyzing the discriminant, you can determine the nature of the roots of the given quadratic equation.
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If 2x square -(2+k)x +k=0 ,where k is a real no. ,find the roots of the equation.? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about If 2x square -(2+k)x +k=0 ,where k is a real no. ,find the roots of the equation.? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If 2x square -(2+k)x +k=0 ,where k is a real no. ,find the roots of the equation.?.
If 2x square -(2+k)x +k=0 ,where k is a real no. ,find the roots of the equation.? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about If 2x square -(2+k)x +k=0 ,where k is a real no. ,find the roots of the equation.? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If 2x square -(2+k)x +k=0 ,where k is a real no. ,find the roots of the equation.?.
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