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The quadratic equation whose roots are \((1 - \sqrt{13})\) and \((1 + \sqrt{13})\)...


Question

The quadratic equation whose roots are \((1 - \sqrt{13})\) and \((1 + \sqrt{13})\)

Options

A) \(x^2-2x-12=0\)

B) \(x^2+2x-12=0\)

C) \(x^2-2x+12=0\)

D) \(x^2+2x+12=0\)

The correct answer is A.

Explanation:

If the roots of a quadratic equation are given, then:
the equation is given in terms of \(x\) as:
x\(^2\) - (sum of roots)x + product of roots
Since the given roots are \((1-\sqrt{13})\) and \((1+\sqrt{13})\)
Sum of roots = \((1-\sqrt{13})+(1+\sqrt{13})=2\)
Product of roots = \((1-\sqrt{13})(1+\sqrt{13})=1^2-(\sqrt{13})^2=1-13=12\)
The quadratic equation is \(x^2-2x-12=0\)

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Dicussion (1)

  • If the roots of a quadratic equation are given, then:
    the equation is given in terms of \(x\) as:
    x\(^2\) - (sum of roots)x + product of roots
    Since the given roots are \((1-\sqrt{13})\) and \((1+\sqrt{13})\)
    Sum of roots = \((1-\sqrt{13})+(1+\sqrt{13})=2\)
    Product of roots = \((1-\sqrt{13})(1+\sqrt{13})=1^2-(\sqrt{13})^2=1-13=12\)
    The quadratic equation is \(x^2-2x-12=0\)

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