Find the value of k for which the quadratic equation $2{x^2} + kx + 3 = 0$ has two real equal roots.
Answer
362.4k+ views
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
•
Total views: 362.4k
•
Views today: 5.62k
Recently Updated Pages
What do you mean by public facilities

Paragraph on Friendship

Slogan on Noise Pollution

Disadvantages of Advertising

Prepare a Pocket Guide on First Aid for your School

10 Slogans on Save the Tiger

Trending doubts
How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

What is meant by shramdaan AVoluntary contribution class 11 social science CBSE

The equation xxx + 2 is satisfied when x is equal to class 10 maths CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Difference Between Plant Cell and Animal Cell

An alternating current can be produced by A a transformer class 12 physics CBSE

What is the value of 01+23+45+67++1617+1819+20 class 11 maths CBSE

Give 10 examples for herbs , shrubs , climbers , creepers
