Question

if the roots of x2-bx+c=0 are two consecutive integers ,then b^2-4c =

Answer 1

(x - a)(x - a - 1)
= x² - (a + 1)x - ax + a(a + 1)
= x² - (2a + 1)x + a(a + 1) 
then 
b² - 4c = (2a + 1)² - 4a(a + 1)
= 4a² + 1 + 4a - 4a² - 4a
= 1

Answer 2

Answer:

Step-by-step explanation:

Given equation is x

x^2 −bx+c=0

Let the roots be α and α+1

Therefore, 2α+1=b

⇒α(α+1)=c

Hence, b2 −4c

=(2α+1)2 −4α(α+1)

=1