Question

if both zeros of a quadratic polynomial p(x) = (k +2)x^2 - (k - 2)x - 5 are equal in magnitude but opposite in sign then find the value of k

ITS URGENT

Answer 1

Let one zero of the above polynomial be @

ATQ,

Other Zero would be -@

We have,

p(x)=(k+2)² -(k-2)x -5

Sum of Zeros: - x coefficient/x²coefficient

@+(-@) = -[-(k-2)]/(k+2)

→0=(k-2)/(k+2)

→k-2=0

→k=2

For k=2,the above quadratic polynomial has zeros equal in magnitude and opposite in sign

Answer 2

We have , p(x) = (k+2)x^2 - (k-2)x - 5 is a quadratic polynomial having zeros which are equal in magnitude but opposite in sign.

.) Now we have to find the value of 'k'

Now , let zeros be 'X = x' and 'Y = -x'          ..........(1)

Here , a = k+2 , b = -(k-2) , c = -5                  .........(2)  

.) We know  that in quadratic equation ,

sum of zeros = X + Y = -b / a                      ............(3)

product of zeros = X*Y =c / a                       .............(4)

.) Now using (1) and (2) in (3) , we get

x + (-x) = (k-2) / (k+2)  

=> 0 = (k-2)/(k+2)

=> k-2 = 0

=> k = 2

Hence , value of k is 2