Question

If one zero of the quadratic polynomial f(x)= 4x 2 -8kx -9 is negative of the other, find the value of k.

Answer 1

Let a be on of the zero of the polynomial,
According to the question, the other zero of the polynomial is -a,

Sum of Zeroes of the polynomial = a + (-a) = a-a = 0,

We know that, If a quadratic equation such as  ax² + bx + c, Then the sum of zeroes of polynomial is -b/a ,

Now from this statement, Sum of Zeroes of given Polynomial is -(-8k)/4,
We can equal them, Since both are sum of zeroes of Polynomial ! 

=> 8k/4 = 0,
=> 2k = 0,
=> k = 0,

Therefore the value of k is 0,

Hope you understand, Have a Great Day, Merry Christmas !
Thanking you, Bunti 360 !

Answer 2

Answer :-

→ k = 0 .

Step-by-step explanation :-

It is given that,

→ One zeros of the given polynomial is negative of the other .

Let one zero of the given polynomial be x .

Then, the other zero is -x .

•°• Sum of zeros = x + ( - x ) = 0 .

But, Sum of zeros = -( coefficient of x )/( coefficient of x² ) = - ( -8k )/4 .

==> 2k = 0 .

==> k = 0/2 .

•°• k = 0 .

Hence, it is solved.