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If roots of the equation x2 – bx + c = 0 be two consectutive integers, then b2 – 4c equals ?

If roots of the equation x2 – bx + c = 0 be two consectutive integers, then b2 – 4c equals ?

Grade:12

2 Answers

Arun
25750 Points
3 years ago

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

Vikas TU
14149 Points
3 years ago
(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

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