Question

if sum of zeros of the quadratic equation k x square - 2 x minus 3 K is equal to their product find the value of k​

Answer 1

Answer :

k = -2/3

Step-by-step explanation :

➤ Quadratic Polynomials :

 ✯ It is a polynomial of degree 2

 ✯ General form :

           ax² + bx + c  = 0

 ✯ Determinant, D = b² - 4ac

 ✯ Based on the value of Determinant, we can define the nature of roots.

         D > 0 ; real and unequal roots

         D = 0 ; real and equal roots

         D < 0 ; no real roots i.e., imaginary

 ✯ Relationship between zeroes and coefficients :

           ✩ Sum of zeroes = -b/a

           ✩ Product of zeroes = c/a

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Given quadratic polynomial,

kx² - 2x - 3k

It is of the form ax² + bx + c

 a = k , b = -2 , c = -3k

     

we know,

Sum of zeroes = -b/a

Product of zeroes = c/a

given,

Sum of zeroes = Product of zeroes

              -b/a     =   c/a

                 -b     =    c

               -(-2)  =  -3k

                   2 = -3k

                   -3k = 2

                   k = -2/3

The value of k is -2/3

Answer 2

Answer:

-2/3 is the correct answer