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प्रश्न
A quadratic equation whose one root is 2 and the sum of whose roots is zero, is ______.
विकल्प
x2 + 4 = 0
x2 − 4 = 0
4x2 − 1 = 0
x2 − 2 = 0
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उत्तर
A quadratic equation whose one root is 2 and the sum of whose roots is zero, is x2 − 4 = 0.
Explanation:
Let α and β be the roots of quadratic equation in such a way that a = 2
Then, according to question sum of the roots
α + β = 0
2 + β = 0
β = – 2
And the product of the roots
α . β = 2 × (– 2)
= – 4
As we know that the quadratic equation
x2 – (α + β) x + αβ = 0
Putting the value of α and β in above
Therefore, the require equation be
x2 − 0 × x + (− 4) = 0
x2 − 4 = 0
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