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Standard XI

Mathematics

Nature of Roots

If a,c∈ℕ and ...

Question

If $a, c \in N$ and both the roots of the equation $a x^{2} - 5 x + c = 0$ are real, then both roots must be

Positive

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Data in sufficient

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Opposite in sign

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Negative

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Solution

The correct option is A Positive
$a x^{2} - 5 x + c = 0, a, c \in N$
Sum of roots
$= \frac{5}{a} > 0 (∵ a \in N)$
Product of roots
$= \frac{c}{a} > 0 (∵ a, c \in N)$

So, both the roots have to be positve.

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Similar questions

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Nature of Roots

Standard XI Mathematics

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If a,c∈N and both the roots of the equation ax2−5x+c=0 are real, then both roots must be

The correct option is A Positiveax2−5x+c=0, a,c∈N Sum of roots =5a>0 (∵a∈N) Product of roots =ca>0 (∵a,c∈N) So, both the roots have to be positve.

If $a, c \in N$ and both the roots of the equation $a x^{2} - 5 x + c = 0$ are real, then both roots must be

The correct option is A Positive
$a x^{2} - 5 x + c = 0, a, c \in N$
Sum of roots
$= \frac{5}{a} > 0 (∵ a \in N)$
Product of roots
$= \frac{c}{a} > 0 (∵ a, c \in N)$

So, both the roots have to be positve.