Let Z 1 and Z 2 be complex numbers such that z 12-4 z 2-16-20 i- Suppose that - - rae roots of t 2- z 1 t - z 2- m -0 for some complex number -m- satisfying -2 -7- Then greatest value of - m - isA- 5-21B- 5-23C- 7-43D- 7-41

The correct option is D α + β = Z, αβ = Z_2 + m (α β)^2 = Z_1^2 4Z_2 4m = 16 + 20i 4m |α nbsp; β | = 2√(7) ⇒ 28 = |(16 4m)+20i| |m (4+5i)| = 7 Great ...

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Byju's Answer

Standard XII

Mathematics

Equality of 2 Complex Numbers

Let Z 1 and Z...

Question

Let $Z_{1}$ and $Z_{2}$ be complex numbers such that $z_{1}^{2} - 4 z_{2}$ = 16 + 20i. Suppose that $α, β$ rae roots of $t^{2} + z_{1} t + z_{2} + m$ = 0 for some complex number 'm' satisfying $| α - β |$ = $2 \sqrt{7}$ . Then greatest value of |m| is

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Solution

The correct option is D

$α + β$ = -Z, $α β$ = $Z_{2} + m$

$(α - β)^{2}$ = $Z_{1}^{2} - 4 Z_{2} - 4 m$

= 16 + 20i - 4m

$| α - β |$ = $2 \sqrt{7}$ $\Rightarrow 28$ = $| (16 - 4 m) + 20 i |$

$| m - (4 + 5 i) |$ = 7

Greatest value of |m| is $7 + \sqrt{41}$

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Let Z1 and Z2 be complex numbers such that z21−4z2 = 16 + 20i. Suppose that α,β rae roots of t2+z1t+z2+m = 0 for some complex number 'm' satisfying |α−β| = 2√7. Then greatest value of |m| is

The correct option is D α+β = -Z, αβ = Z2+m (α−β)2 = Z21−4Z2−4m = 16 + 20i - 4m |α−β| = 2√7 ⇒28 = |(16−4m)+20i| |m−(4+5i)| = 7 Greatest value of |m| is 7+√41

Let $Z_{1}$ and $Z_{2}$ be complex numbers such that $z_{1}^{2} - 4 z_{2}$ = 16 + 20i. Suppose that $α, β$ rae roots of $t^{2} + z_{1} t + z_{2} + m$ = 0 for some complex number 'm' satisfying $| α - β |$ = $2 \sqrt{7}$ . Then greatest value of |m| is

The correct option is D

$α + β$ = -Z, $α β$ = $Z_{2} + m$

$(α - β)^{2}$ = $Z_{1}^{2} - 4 Z_{2} - 4 m$

= 16 + 20i - 4m

$| α - β |$ = $2 \sqrt{7}$ $\Rightarrow 28$ = $| (16 - 4 m) + 20 i |$

$| m - (4 + 5 i) |$ = 7

Greatest value of |m| is $7 + \sqrt{41}$