Question

for what value of k, the quadratic equation 2x2 + kx + 3 = 0 has equal root?

Answer 1

Given Equation

• 2x² + kx + 3 = 0
• It has equal roots.

⠀

To find

• Value of k if the Quadratic Equation has equal roots.

⠀

Solution

• As it is given in the question that the quadratic equation has equal roots.
• We know that, if roots are equal, then

$\large\: \: \: \: \: \: \: {\green{\boxed{\bf{\red{Discriminant (D) = 0}}}}}$

⠀

★ Formula of discriminant

$\: \: \: \: \: \: \: \: \: \: \: \: \boxed{\tt{\bigstar{D_{(discriminant)} = b^2 - 4ac{\bigstar}}}}$

⠀

Here

• a = 2
• b = k
• c = 3

⠀

★ Calculating discriminant

$\tt\longmapsto{D = (k)^2 - 4(2)(3) = 0}$

⠀

$\tt\longmapsto{k^2 - 24 = 0}$

⠀

$\tt\longmapsto{k^2 = 24}$

⠀

$\tt\longmapsto{k = \sqrt{24}}$

⠀

$\large{\bf{\longmapsto{k = ±2\sqrt{6}}}}$

⠀

Therefore,

• The value of k is ±2√6.

━━━━━━━━━━━━━━━━━━━━━━