If roots of the equation x2 – bx + c = 0 be two consectutive integers, then b2 – 4c equals ?
sudhanshu , 11 Years ago
Grade 12
Engineering Entrance Exams> If roots of the equation x2 – bx + c = 0 ...
2 Answers
Arun
Last Activity: 5 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
Last Activity: 5 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
= 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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