For the quadratic equation ax 2- bx - c -0- a - b - c - R if b 2-4 ac -0 and ac -0- then which of the following is always true -A- Roots are always negativeB- Roots are always positiveC- Roots are of same signD- Roots are of opposite sign

The correct option is C Roots are of same signax^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 ⇒ ...

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Standard XIII

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

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Roots are always positive

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Roots are of same sign

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Roots are of opposite sign

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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.

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Similar questions

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Nature of Roots

Standard XIII 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 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.