If is a root of the quadratic equation 4x 2 - 4kx + k + 5 = 0 , then the value of k is 1. -6 2. -3 3. 3 4. 6

Given , is a root of the quadratic equation 4x 2 - 4kx + k + 5 = 0 ∴ Option 4 is the correct option

Mathematics

If $\dfrac{1}{2}$ is a root of the quadratic equation 4x² - 4kx + k + 5 = 0 , then the value of k is
-6
-3
3
6

Quadratic Equations

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Answer

Given ,

$\dfrac{1}{2}$ is a root of the quadratic equation 4x² - 4kx + k + 5 = 0

$\therefore 4\Big(\dfrac{1}{2}\Big)^2 - 4k\Big(\dfrac{1}{2}\Big) + k + 5 = 0 \\[0.5em] \Rightarrow 1 - 2k + k + 5 = 0 \\[0.5em] \Rightarrow -k + 6 = 0 \\[0.5em] k = 6$

∴ Option 4 is the correct option

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Mathematics

If $\dfrac{1}{2}$ is a root of the quadratic equation 4x² - 4kx + k + 5 = 0 , then the value of k is
-6
-3
3
6

Quadratic Equations

Answer

Related Questions

If twice the area of a smaller square is subtracted from the area of a larger square, the result is 14cm². However, if twice the area of the larger square is added to three times the area of the smaller square, the result is 203 cm². Determine the sides of two squares.

Which of the following is not a quadratic equation?
(x + 2)² = 2(x + 3)
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The roots of the equation x² - 3x - 10 = 0 are
2, -5
-2, 5
2, 5
-2, -5

If one root of a quadratic equation with rational coefficients is $\dfrac{3 - \sqrt{5}}{2}$ , then the other root is
$\dfrac{-3 - \sqrt{5}}{2}$
$\dfrac{-3 + \sqrt{5}}{2}$
$\dfrac{3 + \sqrt{5}}{2}$
$\dfrac{\sqrt{3} + 5}{2}$

Mathematics

If 12\dfrac{1}{2}21​ is a root of the quadratic equation 4x2 - 4kx + k + 5 = 0 , then the value of k is-6-336

Quadratic Equations

Answer

Related Questions

If twice the area of a smaller square is subtracted from the area of a larger square, the result is 14cm2. However, if twice the area of the larger square is added to three times the area of the smaller square, the result is 203 cm2. Determine the sides of two squares.

Which of the following is not a quadratic equation?(x + 2)2 = 2(x + 3)x2 + 3x = (-1)(1 - 3x)(x + 2)(x - 1) = x2 - 2x - 3x3 - x2 + 2x + 1 = (x + 1)3

The roots of the equation x2 - 3x - 10 = 0 are2, -5-2, 52, 5-2, -5

If one root of a quadratic equation with rational coefficients is 3−52\dfrac{3 - \sqrt{5}}{2}23−5​​, then the other root is−3−52\dfrac{-3 - \sqrt{5}}{2}2−3−5​​−3+52\dfrac{-3 + \sqrt{5}}{2}2−3+5​​3+52\dfrac{3 + \sqrt{5}}{2}23+5​​3+52\dfrac{\sqrt{3} + 5}{2}23​+5​

If $\dfrac{1}{2}$ is a root of the quadratic equation 4x² - 4kx + k + 5 = 0 , then the value of k is
-6
-3
3
6

If twice the area of a smaller square is subtracted from the area of a larger square, the result is 14cm². However, if twice the area of the larger square is added to three times the area of the smaller square, the result is 203 cm². Determine the sides of two squares.

Which of the following is not a quadratic equation?
(x + 2)² = 2(x + 3)
x² + 3x = (-1)(1 - 3x)
(x + 2)(x - 1) = x² - 2x - 3
x³ - x² + 2x + 1 = (x + 1)³

The roots of the equation x² - 3x - 10 = 0 are
2, -5
-2, 5
2, 5
-2, -5

If one root of a quadratic equation with rational coefficients is $\dfrac{3 - \sqrt{5}}{2}$ , then the other root is
$\dfrac{-3 - \sqrt{5}}{2}$
$\dfrac{-3 + \sqrt{5}}{2}$
$\dfrac{3 + \sqrt{5}}{2}$
$\dfrac{\sqrt{3} + 5}{2}$