If a- c - N and both the roots of the equation ax 2-5 x - c -0 are real- then both roots must beA- NegativeB- PositiveC- Data in sufficientD- Opposite in sign

The correct option is B Positiveax^2 5x+c=0, a,c∈ℕ Sum of roots = 5a 0 (∵ a∈ℕ) Product of roots nbsp; = c a 0 (∵ a,c∈ℕ) So, both the roots have to be ...

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Standard XIII

Mathematics

Discriminant

If a, c ∈ N a...

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

Negative

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Positive

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Opposite in sign

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Data in sufficient

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Solution

The correct option is B 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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Discriminant

Standard XIII 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 B 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 B 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.