If one root of the quadratic equation ax 2- bx - c -0 - a - b - c - R is reciprocal of the other- then which one of the following is correct-A- a-b-0 B- b - cC- a - CD- a-c-0

The correct option is D a+c=0ax^2 bx c=0; a,b,c∈ℝ Since, this is a quadratic equation, so a0. Let the roots be α and 1α. So, product of roots is, α×1α= ca ⇒ a ...

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Standard XII

Mathematics

Nature of Roots

If one root o...

Question

If one root of the quadratic equation $a x^{2} - b x - c = 0; a, b, c \in R$ is reciprocal of the other, then which one of the following is correct?

a + b = 0

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b = c

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a = c

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a + c = 0

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Solution

The correct option is D $a + c = 0$
$a x^{2} - b x - c = 0; a, b, c \in R$
Since, this is a quadratic equation, so $a \neq 0$ .
Let the roots be $α$ and $\frac{1}{α}$ .
So, product of roots is,
$α \times \frac{1}{α} = - \frac{c}{a}$
$\Rightarrow a = - c$
$\Rightarrow a + c = 0$

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Nature of Roots

Standard XII Mathematics

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If one root of the quadratic equation ax2−bx−c=0; a,b,c∈R is reciprocal of the other, then which one of the following is correct?

The correct option is D a+c=0ax2−bx−c=0; a,b,c∈R Since, this is a quadratic equation, so a≠0. Let the roots be α and 1α. So, product of roots is, α×1α=−ca ⇒a=−c ⇒a+c=0

If one root of the quadratic equation $a x^{2} - b x - c = 0; a, b, c \in R$ is reciprocal of the other, then which one of the following is correct?

The correct option is D $a + c = 0$
$a x^{2} - b x - c = 0; a, b, c \in R$
Since, this is a quadratic equation, so $a \neq 0$ .
Let the roots be $α$ and $\frac{1}{α}$ .
So, product of roots is,
$α \times \frac{1}{α} = - \frac{c}{a}$
$\Rightarrow a = - c$
$\Rightarrow a + c = 0$