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Relation between Roots and Coefficients for Quadratic

If the differ...

Question

If the different of the roots of $x^{2} - p x + q = 0$ is unity, then

$p^{2} + 4 q = 1$

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$p^{2} - 4 q = 1$

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$p^{2} + 4 q^{2} = (1 + 2 q)^{2}$

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$4 p^{2} + q^{2} = (1 + 2 p)^{2}$

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Solution

The correct option is A
$p^{2} + 4 q = 1$

Given equation: $x^{2} - p x + q = 0$ Also, $α$ and $β$ are the roots of the equation such that $α - β$ = 1. sum of the roots = $α + β$ = $\frac{- C o e f f i c i e n t o f x}{C o e f f i c i e n t o f x^{2}} = - (\frac{- p}{1}) = p$ Product of the roots = $α β α β = \frac{C o n s t a n t t e r m}{C o e f f e c i e n t o f x^{2}} = q ∴ (α + β)^{2} - (α - β)^{2} = 4 α β \Rightarrow p^{2} - 1 \Rightarrow p^{2} - 4 q = 1$

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Similar questions

x^{2} - p x + q = 0

x^{2} - p x + q = 0

p^{2} + 4 q = 1

p^{2} - 4 q = 1

p^{2} + 4 q^{2} = (1 + 2 q)^{2}

4 p^{2} + q^{2} = (1 + 2 p)^{2}

x^{2} - p x + q = 0

p^{2} - 4 q = 1

p^{2} + 4 q^{2} = {(1 + 2 q)}^{2}

x^{2} + p x + q = 0

α

β

x^{2} + p x + q = 0

(ω α + ω^{2} β) (ω^{2} α + ω β)

ω

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