Solveeit Logo
Login

Question

Question: If α, β\((\alpha < \beta)\) are roots of the equation \(x^{2} + bx + c = 0\) where \((c < 0 < b)\) t...

If α, β(α<β)(\alpha < \beta) are roots of the equation x2+bx+c=0x^{2} + bx + c = 0 where (c<0<b)(c < 0 < b) then

A

0<α<β0 < \alpha < \beta

B

α<0<β<∣α∣\alpha < 0 < \beta < |\alpha|

C

α<β<0\alpha < \beta < 0

D

α<0<∣α∣<β\alpha < 0 < |\alpha| < \beta

Answer

α<0<β<∣α∣\alpha < 0 < \beta < |\alpha|

Explanation

Solution

Since f(0)=0+0+c=c<0f(0) = 0 + 0 + c = c < 0

∴ Roots will be of opposite sign, α+β=−b=−ve\alpha + \beta = - b = - ve

(b > 0)

It is given that α<β\alpha < \beta

So, α+β=−ve\alpha + \beta = - ve is possible only when ∣α∣>β|\alpha| > \beta

⇒ α<0,β>0,∣α∣>β\alpha < 0,\beta > 0,|\alpha| > \beta ⇒ α<0<β<∣α∣\alpha < 0 < \beta < |\alpha|