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 ...

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Standard XI

Mathematics

Roots under Different Values of Coefficients

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 of same sign

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Roots are of opposite sign

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Roots are always negative

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Roots are always positive

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Solution

The correct option is A 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.

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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. 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 ?

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

and a, b, c are all positive, then

Q. If

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is-

Q. For the quadratic equation

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

, if

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

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Roots under Different Values of Coefficients

Standard XI Mathematics

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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 A 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 A 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.