Question

find the value of k for which the quadratic equation 2x^+kx+3=0 has two equal roots

Answer 1

2x²+kx+3=0
where,
a=2
b=k
c=3
it has two equal roots,
D=0
now, by quadratic formula,
D=b²-4ac
0=(k)²-4(2)(3)
0=k²-24
24=k²
±√24=k

the value of k is ±√24

hope this answer will help you

Answer 2

Question:

Find the value of k for which the quadratic equation 2x²+ kx + 3=0 has equal roots.

Answer:

k = ± 2√6

Note:

• An equation of degree 2 is know as quadratic equation .

• Roots of an equation is defined as the possible values of the unknown (variable) for which the equation is satisfied.

• The maximum number of roots of an equation will be equal to its degree.

• A quadratic equation has atmost two roots.

• The general form of a quadratic equation is given as , ax² + bx + c = 0 .

• The discriminant of the quadratic equation is given as , D = b² - 4ac .

• If D = 0 , then the quadratic equation would have real and equal roots .

• If D > 0 , then the quadratic equation would have real and distinct roots .

• If D < 0 , then the quadratic equation would have imaginary roots .

Solution:

The given quadratic equation is ;

2x² + kx + 3 = 0 .

Clearly , we have ;

a = 2

b = k

c = 3

We know that ,

The quadratic equation will have real and equal roots if its discriminant is zero .

=> D = 0

=> b² - 4ac = 0

=> k² - 4•2•3 = 0

=> k² - 24 = 0

=> k² = 24

=> k = √24

=> k = ± 2√6

Hence,

Hence,The required values of k are ± 2√6 .