If the equation, <math> <msup> <mrow> <mrow> <mi>x</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msup> <mo>+</mo> <mi>b</mi> <mi>x</mi> <mo>+</mo> <mn>45</mn> <mo>=</mo> <mn>0</mn> <mo>(</mo> <mi>b</mi> <mo>∈</mo> <mi>R</mi> <mo>)</mo> </math> <math><msup><mrow><mrow></mrow></mrow><mrow><mrow></mrow></mrow></msup></math>&nbsp;has conjugate complex roots and they satisfy&nbsp;<math><mroot><mrow><mrow></mrow></mrow></mroot></math> <math> <mo>|</mo> <mi>z</mi> <mo>+</mo> <mn>1</mn> <mo>|</mo> <mo>=</mo> <mn>2</mn> <mroot> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow></mrow> </mroot> </math> , then:

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Maths Class 11th Ncert Solutions Maths class 11th

If the equation, $x^{2} + b x + 45 = 0 (b \in R)$ $^{}$ has conjugate complex roots and they satisfy $| z + 1 | = 2 \sqrt[]{10}$ , then:

Option 1 -

$b^{2} + b = 12$

Option 2 -

$b^{2} - b = 42$

Option 3 -

$b^{2} - b = 30$

Option 4 -

$b^{2} + b = 72$

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Answered by

Raj Pandey | Contributor-Level 9

a month ago

Correct Option - 3

Detailed Solution:

Let z = α ± iβ be roots of the equation
So 2α = -b and α² + β² = 45, (α+1)² + β² = 40
So (α+1)² - α² = -5 ⇒ 2α+1 = -5 ⇒ 2α = -6
So b=6
Hence b² - b = 30

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If the equation, $x^{2} + b x + 45 = 0 (b \in R)$ $^{}$ has conjugate complex roots and they satisfy $| z + 1 | = 2 \sqrt[]{10}$ , then:

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If the equation, x 2 + b x + 45 = 0 ( b ∈ R ) has conjugate complex roots and they satisfy | z + 1 | = 2 10 , then:

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If the equation, $x^{2} + b x + 45 = 0 (b \in R)$ $^{}$ has conjugate complex roots and they satisfy $| z + 1 | = 2 \sqrt[]{10}$ , then: