Assertion -If the equation ax2 - bx - c - 0- 0 1- -z2- - 1- Reason- Complex roots always occur in conjugate pairs-

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Standard XII

Mathematics

Properties of Conjugate of a Complex Number

Assertion :If...

Question

Assertion :If the equation $a x^{2} + b x + c = 0$ , $0 < a < b < c,$ has non real complex roots $z_{1}$ and $z_{2}$ , then $| z_{1} | > 1$ , $| z_{2} | > 1$ . Reason: Complex roots always occur in conjugate pairs.

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

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Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

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Assertion is correct but Reason is incorrect

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Assertion is incorrect and Reason is correct

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Solution

The correct option is B Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
Roots of equation $a x^{2} + b x + c = 0$
$z_{1} = \frac{- b + \sqrt{b^{2} - 4 a c}}{2 a}$
$z_{2} = \frac{- b - \sqrt{b^{2} - 4 a c}}{2 a}$
$| z_{1} |, | z_{2} |$ must greater than one.
and reason is also correct.
and it is property of complex function that they always occur in conjugate root.
so modulus of $z_{1}$ and $z_{2}$ will be equal and greater than one.

Option B is correct.

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Similar questions

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Assertion :If the equation ax2+bx+c=0, 0<a<b<c, has non real complex roots z1 and z2, then |z1|>1, |z2|>1. Reason: Complex roots always occur in conjugate pairs.

Assertion :If the equation $a x^{2} + b x + c = 0$ , $0 < a < b < c,$ has non real complex roots $z_{1}$ and $z_{2}$ , then $| z_{1} | > 1$ , $| z_{2} | > 1$ . Reason: Complex roots always occur in conjugate pairs.