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

# 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) $$x^2+2x+12=0$$

### 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 $$x^2-2x-12=0$$

## 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 $$x^2-2x-12=0$$