Question

Find the values of k for which the quadratic equation 4x^+5kx+25=0 has equal roots

Answer 1

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Answer 2

Question:

Find the value of k for which the quadratic equation 4x² + 5kx + 25 = 0 has equal roots.

Answer:

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 ;

4x² + 5kx + 25 = 0

Clearly , we have ;

a = 4

b = 5k

c = 25

We know that ,

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

=> D = 0

=> (5k)² - 4•4•25 = 0

=> 25k² - 4•4•25 = 0

=> 25(k² - 4•4) = 0

=> k² - 16 = 0

=> k² = 16

=> k = √16

=> k = ± 4

Hence,

The required values of k are ± 4 .