If $α$ and $β (α < β)$ are the roots of the equation $x^{2} + b x + c = 0$ , where $c < 0 < b$ , then

0 < α < β

No worries! We‘ve got your back. Try BYJU‘S free classes today!

α < 0 < β < |α|

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

α < β < 0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

α < 0 < |α| < β

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B α < 0 < β < |α|
Here $D = b^{2} - 4 a c > 0$ because $c < 0 < b$ .
So roots are real and unequal.
Now, $α + β = - b < 0$ and $α β = c < 0$
Therefore, One root is positive and the other negative, the negative root being numerically bigger.
As $α < β, α$ is the negative root while $β$ is the positive root.
So, $| α | > β$ and $α < 0 < β$ .

Suggest Corrections

Similar questions

Q. If

α a n d β

(

α < β

) are the roots of equation

x^{2} + 2 x - 5 = 0

, then the value of

\frac{1}{α} - \frac{1}{β}

is:

Let $α$ and $β$ ( $α < β$ ) be roots of the quadratic equation $a x^{2} + b x + c = 0.$ If 0 < a < c and a + c = b, then which of the following statement(s) is/are correct?

Let $k$ be the non-zero real number such that the quadratic equations $k x^{2} + 2 x + k = 0$ has two distinct real roots $α a n d β (α < β) .$

If $β < \sqrt{2} + α$ , then

Q. Let

a > b > 0

and the quadratic equation

a x^{2} + b x - 9 = 0

has roots as

α, β (α < β) .

a^{3} + b^{3} + 27 a b = 729,

then the value of

4 β - a α

Q. If the points

(α - x, α, α)

(α, α - y, α)

(α, α, α - z)

and

(α - 1, α - 1, α - 1)

are coplanar

α \in R

then

Join BYJU'S Learning Program

If α and β(α<β) are the roots of the equation x2+bx+c=0, where c<0<b, then

If $α$ and $β (α < β)$ are the roots of the equation $x^{2} + b x + c = 0$ , where $c < 0 < b$ , then