For the quadratic equation ax2-bx-c-0- a-b-c- if b2-4ac-0 and ac-0- then which of the following is always true -

Ax^2+bx+c=0, a,b,c∈ℝ Given nbsp;b^2 4ac gt;0 and ac gt;0 Since, a0 Dividing by a^2 both the sides, we get ⇒ ca gt;0 ⇒ Product of roots is greater than 0 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XI

Mathematics

Nature of Roots

For the quadr...

Question

For the quadratic equation $a x^{2} + b x + c = 0, a, b, c \in R$ if $b^{2} - 4 a c > 0$ and $a c > 0,$ then which of the following is always true ?

Roots are always negative

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

Roots are always positive

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

Roots are of same sign

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

Roots are of opposite sign

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

Open in App

Solution

The correct option is C Roots are of same sign
$a x^{2} + b x + c = 0, a, b, c \in R$
Given $b^{2} - 4 a c > 0$
and $a c > 0$
Since, $a \neq 0$
Dividing by $a^{2}$ both the sides, we get
$\Rightarrow \frac{c}{a} > 0$
$\Rightarrow$ Product of roots is greater than $0.$
Hence, roots are of same sign.

Suggest Corrections

Similar questions

Q. For the quadratic equation

a x^{2} + b x + c = 0, a, b, c \in R

b^{2} - 4 a c > 0

and

a c > 0,

then which of the following is always true ?

Q. If, for quadratic equation

a x^{2} + b x + c = 0, b^{2} - 4 a c ≰ 0

and a, b, c are all positive, then

Q. If

b^{2} - 4 a c \geq 0

then the roots of quadratic equation

a x^{2} + b x + c = 0

is-

Q. What is the nature of the roots of the quadratic equation

a x^{2} + b x + c = 0

if
(a)

b^{2} - 4 a c = 0

(b)

b^{2} - 4 a c < 0

Q. For the quadratic equation

a x^{2} + b x + c = 0

, if

b^{2} - 4 a c > 0

and

a, c

have same sign, then which of the following is true?

(a, b, c \in R, a \neq 0)

Join BYJU'S Learning Program

Explore more

Nature of Roots

Standard XI Mathematics

Join BYJU'S Learning Program

For the quadratic equation ax2+bx+c=0, a,b,c∈R if b2−4ac>0 and ac>0, then which of the following is always true ?

The correct option is C Roots are of same signax2+bx+c=0, a,b,c∈R Given b2−4ac>0 and ac>0 Since, a≠0 Dividing by a2 both the sides, we get ⇒ca>0 ⇒ Product of roots is greater than 0. Hence, roots are of same sign.

For the quadratic equation $a x^{2} + b x + c = 0, a, b, c \in R$ if $b^{2} - 4 a c > 0$ and $a c > 0,$ then which of the following is always true ?

The correct option is C Roots are of same sign
$a x^{2} + b x + c = 0, a, b, c \in R$
Given $b^{2} - 4 a c > 0$
and $a c > 0$
Since, $a \neq 0$
Dividing by $a^{2}$ both the sides, we get
$\Rightarrow \frac{c}{a} > 0$
$\Rightarrow$ Product of roots is greater than $0.$
Hence, roots are of same sign.