Question

find the value of k for which the quadratic equation 2x2+kx+2=0has equal roots

Answer 1

Given Equation

• 2x² + kx + 2 = 0

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To find

• Value of k.

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Solution

• We know that, when the quadratic equation has equal roots then

$\large{\boxed{\boxed{\sf{Discriminant = 0}}}}$

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• Let's find the discriminant

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$\: \: \: \: \: \: \: \: \: \: \: \: \boxed{\tt{\bigstar{D = b^2 - 4ac{\bigstar}}}}$

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Here,

• a = 2
• b = k
• c = 2

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$\tt:\implies\: \: \: \: \: \: \: \: {D = (k)^2 - 4(2)(2)}$

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$\tt:\implies\: \: \: \: \: \: \: \: {D = k^2 - 16}$

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• Since, roots are equal

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$\mathcal:\implies\: \: \: \: \: \: \: \: {D = 0}$

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$\tt:\implies\: \: \: \: \: \: \: \: {k^2 - 16 = 0}$

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$\tt:\implies\: \: \: \: \: \: \: \: {k^2 = 16}$

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$\tt:\implies\: \: \: \: \: \: \: \: {k = \sqrt{16}}$

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$\bf:\implies\: \: \: \: \: \: \: \: {k = ±4}$

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Hence,

• The value of k is ±4.

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