The solution set for the quadratic equation 2x^2 + kx - k^2 = 0 is: 1. {k, k} 2. {-k, k} 3. {-k, k/2} 4. {-k/2, k}

⇒ 2x2 + kx - k2 = 0 ⇒ 2x2 + 2kx - kx - k2 = 0 ⇒ 2x(x + k) - k(x + k) = 0 ⇒ (2x - k)(x + k) = 0 ⇒ 2x - k = 0 or x + k = 0 [Using Zero-product rule] ⇒ 2x = k or x = -k ⇒ x = or x = -k The solution set: . Hence, option 3 is the correct option.

Mathematics

The solution set for the quadratic equation 2x² + kx - k² = 0 is:
{k, k}
{-k, k}
$\Big{-k, \dfrac{k}{2}\Big}$
$\Big{\dfrac{-k}{2}, k\Big}$

Quadratic Equations

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Answer

⇒ 2x² + kx - k² = 0

⇒ 2x² + 2kx - kx - k² = 0

⇒ 2x(x + k) - k(x + k) = 0

⇒ (2x - k)(x + k) = 0

⇒ 2x - k = 0 or x + k = 0 [Using Zero-product rule]

⇒ 2x = k or x = -k

⇒ x = $\dfrac{k}{2}$ or x = -k

The solution set: $\Big{-k, \dfrac{k}{2}\Big}$ .

Hence, option 3 is the correct option.

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Mathematics

The solution set for the quadratic equation 2x² + kx - k² = 0 is:
{k, k}
{-k, k}
$\Big{-k, \dfrac{k}{2}\Big}$
$\Big{\dfrac{-k}{2}, k\Big}$

Quadratic Equations

Answer

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1 - $2\sqrt{2}$
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The roots of the equation $x + \dfrac{1}{x}$ = 3 are:
$\dfrac{2 \pm \sqrt{5}}{2}$
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$\Big{-\dfrac{1}{5}, \dfrac{4}{5}\Big}$
$\Big{-\dfrac{4}{5}, -\dfrac{1}{5}\Big}$
$\Big{-\dfrac{4}{5}, \dfrac{1}{5}\Big}$

The value of the discriminant of the equation, 3x² = - 11x - 10, is:
1
0
4
9

Mathematics

The solution set for the quadratic equation 2x2 + kx - k2 = 0 is:{k, k}{-k, k}{−k,k2}\Big{-k, \dfrac{k}{2}\Big}{−k,2k​}{−k2,k}\Big{\dfrac{-k}{2}, k\Big}{2−k​,k}

Quadratic Equations

Answer

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The value of the discriminant of the equation, x2 - (2\sqrt{2}2​ + 1)x + 2\sqrt{2}2​ = 0 is:3 + 222\sqrt{2}22​1 - 222\sqrt{2}22​3 - 222\sqrt{2}22​2 - 2\sqrt{2}2​

The roots of the equation x+1xx + \dfrac{1}{x}x+x1​ = 3 are:2±52\dfrac{2 \pm \sqrt{5}}{2}22±5​​3±52\dfrac{3 \pm \sqrt{5}}{2}23±5​​1±32\dfrac{1 \pm \sqrt{3}}{2}21±3​​none of these

The value of the discriminant of the equation, 3x2 = - 11x - 10, is:1049

The solution set for the quadratic equation 2x² + kx - k² = 0 is:
{k, k}
{-k, k}
$\Big{-k, \dfrac{k}{2}\Big}$
$\Big{\dfrac{-k}{2}, k\Big}$

The value of the discriminant of the equation, x² - ( $\sqrt{2}$ + 1)x + $\sqrt{2}$ = 0 is:
3 + $2\sqrt{2}$
1 - $2\sqrt{2}$
3 - $2\sqrt{2}$
2 - $\sqrt{2}$

The roots of the equation $x + \dfrac{1}{x}$ = 3 are:
$\dfrac{2 \pm \sqrt{5}}{2}$
$\dfrac{3 \pm \sqrt{5}}{2}$
$\dfrac{1 \pm \sqrt{3}}{2}$
none of these

The value of the discriminant of the equation, 3x² = - 11x - 10, is:
1
0
4
9