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Algebra of Roots of Quadratic Equations

If the differ...

Question

If the difference of the roots of $x^{2} - p x + q = 0$ is unity, then the value of $p^{2} - 4 q$ is

A

1.00

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B

1

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C

1.0

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Solution

$x^{2} - p x + q = 0$
Let the roots of the equation be $α, β$
Now, sum and product of the roots is, $α + β = p, α β = q$
$(α - β)^{2} = (α + β)^{2} - 4 α β \Rightarrow 1^{2} = p^{2} - 4 q ∴ p^{2} - 4 q = 1$

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Algebra of Roots of Quadratic Equations

Standard XII Mathematics

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