Identify the relationship between x and a quadratic equation.

April 23, 2026Mathematics

ScanSolve AI Answer

April 23, 2026

Answer

Step 1: Identify the relationship between $x$ and a quadratic equation. The given value for $x$ is $x = \frac{1}{2}(1 - \sqrt{5})$ . Consider the quadratic equation $t^2 - t - 1 = 0$ . Using the quadratic formula, its roots are: $t = \frac{-(-1) \pm \sqrt{(-1)^2 - 4(1)(-1)}}{2(1)} = \frac{1 \pm \sqrt{1+4}}{2} = \frac{1 \pm \sqrt{5}}{2}$ One of these roots is $t = \frac{1 - \sqrt{5}}{2}$ , which is exactly our $x$ . Therefore, $x

Was this helpful?

Need help with your own homework?

Get instant step-by-step solutions to any question. Free to start.

Ask Your Question

Handwritten Step-by-Step Solution

Get this as a handwritten image on WhatsApp — like a tutor wrote it for you.

Try on WhatsApp

More Mathematics Questions

QI need question paper grade maths QInstructions: Answer Any Four (4) Questions. The questions cover Rolle's Theorem, Mean Value Theorem…QGiven NLM = 50^, so QLM = 50^.QThis shape is called a . 12. Its has equal side. 13. It has equal angles. 14. It has symmetry.QComplete the following: This shape is called . All the sides are , It has square area. It has right-…

See all Mathematics questions →

Still have questions?

Quick Answer

Identify the relationship between x and a quadratic equation. The given value for x is x = (1)/(2)(1 - sqrt(5)).

Asked on April 23, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on April 23, 2026

Step 1: Identify the relationship between x and a quadratic equation. The given value for x is x = (1)/(2)(1 - sqrt(5)). Consider the quadratic equation t^2 - t - 1 = 0. Using the quadratic formula, its roots are: t = -(-1) ± sqrt((-1)^2 - 4(1)(-1))2(1) = 1 ± sqrt(1+4)2 = 1 ± sqrt(5)2 One of these roots is t = 1 - sqrt(5)2, which is exactly our x. Therefore, $x