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A quadratic equation is in the form $ax^2+bx+c=0$ . If the roots of the quadratic equation $2x^2-4x+k=0$ are real and equal, find the value of $k$ .

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Quadratic equation with complex roots

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Q. A quadratic equation is in the form

ax^2+bx+c=0

. If the roots of the quadratic equation

2x^2-4x+k=0

are real and equal, find the value of

k

.

Roots Nature Determination: For the roots of the quadratic equation $ax^2 + bx + c = 0$ to be real and equal, the discriminant $(b^2 - 4ac)$ must be equal to zero. This is because the discriminant determines the nature of the roots.
Given Quadratic Equation: The given quadratic equation is $2x^2 - 4x + k = 0$ . Here, $a = 2$ , $b = -4$ , and $c = k$ . We will use the discriminant condition $b^2 - 4ac = 0$ to find the value of $k$ .
Substitute Values: Substitute the values of $a$ , $b$ , and $c$ into the discriminant condition: $(-4)^2 - 4(2)(k) = 0$ .
Calculate Discriminant: Calculate the discriminant: $16 - 8k = 0$ .
Solve for k: Solve for $k$ : $8k = 16$ .
Final Value Calculation: Divide both sides by $8$ to find the value of $k$ : $k = \frac{16}{8}$ .
Final Value Calculation: Divide both sides by $8$ to find the value of $k$ : $k = \frac{16}{8}$ .Calculate the final value of $k$ : $k = 2$ .

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