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Roots of a Quadratic Equation

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

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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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Similar questions

Q. If the difference of the roots of

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

is unity, then the value of

p^{2} - 4 q

Q. If the difference of the roots of

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

is unity, then prove that

p^{2} - 4 q = 1

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

Q. If the difference of the roots of

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

is unity, then
(a)

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}

Q. If the roots of

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

are two consecutive integers, find the value of

p^{2} - 4 q .

Q. If the roots of the equation x² + px + q = 0 differ by 1, prove that p2 = 1 + 4q

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Roots of a Quadratic Equation

Standard XII Mathematics

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