Question

The values of K for which the quadratic equation 2 X square + kx + 2 equal to zero has equal roots is a 4 b + - 4
c -4 d 0

Answer 1

Question:

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

Options:

a). 4

b). ± 4

c). - 4

d). 0

Answer:

option (b)

k = ± 4

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 + 2 = 0 .

Clearly, here we have ;

a = 2

b = k

c = 2

Now ,

The discriminant of the given quadratic equation will be ;

=> D = b² - 4ac

=> D = k² - 4•2•2

=> D = k² - 16 -------(1)

Also,

We know that , the given quadratic equation would have equal roots only if its discriminant is equal to zero.

=> D = 0

=> k² - 16 = 0 { using eq-(1) }

=> k² = 16

=> k = √16

=> k = ± 4

Hence,

The required values of k are ± 4 .