Question

The discriminant of x2 - 3x - k = 0
is 1.The value of x is .......​

Answer 1

Answer:

1 and 2

Step-by-step explanation:

Given equation is x²−3x−k=0  

On comparing with  ax²+bx+c=0  

We have  a=1,b=−3,c=−k  

As we know that  discriminant(D)=b²−4ac  

(−3)²−4×1×(−k)=1  (as given D = 1)

9+4k=1  

4k=1−9  

k=−84  

k=−2  

Now, the equation becomes x²−3x−(−2)=0  

x² - 3x + 2 = 0

We can solve this equation by splitting middle term and quadratic formula

Here, we Solve by splitting middle term

x²−3x+2=0  

x²−(2+1)x+2=0  

x²−2x−x+2=0  

Bytakingcommon  

x(x−2)−1(x−2)=0  

(x−2)(x−1)=0  

product of any two term can be zero only when either of them is zero

Either,  (x−2)=0or(x−1)=0  

This gives  x=2orx=1  

The values of x are 1 & 2