# Find the value of k for which the quadratic equation $2{x^2} + kx + 3 = 0$ has two real equal roots.

Answer

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Hint: Whenever we have to find two equal roots you should know that the discriminant of a quadratic equation with two equal roots is zero.

Complete step-by-step answer:

A quadratic equation $a{x^2} + bx + c = 0$ has two real equal roots when ${b^2} - 4ac = 0$ ( discriminant = 0 )

On comparing ,

${k^2} - 4 \times 2 \times 3 = 0$

${k^2} = 24$

$k = \pm 2\sqrt 6 $

Therefore the equation has two real equal roots for k =$ \pm 2\sqrt 6 $.

Note: The discriminant has to be 0 when the roots are real and equal. If the discriminant is more than 0 then the roots are real and distinct, if it is less than 0 the roots are complex.

Complete step-by-step answer:

A quadratic equation $a{x^2} + bx + c = 0$ has two real equal roots when ${b^2} - 4ac = 0$ ( discriminant = 0 )

On comparing ,

${k^2} - 4 \times 2 \times 3 = 0$

${k^2} = 24$

$k = \pm 2\sqrt 6 $

Therefore the equation has two real equal roots for k =$ \pm 2\sqrt 6 $.

Note: The discriminant has to be 0 when the roots are real and equal. If the discriminant is more than 0 then the roots are real and distinct, if it is less than 0 the roots are complex.

Last updated date: 02nd Oct 2023

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