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Given the equation: \( y = \frac{1}{\sqrt{2}} \) 1 - Edexcel - GCSE Maths - Question 19 - 2022 - Paper 1
Question 19
Given the equation: \( y = \frac{1}{\sqrt{2}} \) 1. Find the equation of the line. 2. Solve the quadratic equation. 3. Analyze the solutions of the given quadra... show full transcript
Worked Solution & Example Answer:Given the equation: \( y = \frac{1}{\sqrt{2}} \) 1 - Edexcel - GCSE Maths - Question 19 - 2022 - Paper 1
Step 1
1. Find the equation of the line.
Answer
To find the equation of the line, we start by noting that our given equation is in the form of a mathematical constant, ( \frac{1}{\sqrt{2}} ). We can express this as:
[ y = \frac{1}{\sqrt{2}} ]
This represents a horizontal line in the Cartesian plane where the value of ( y ) is always ( \frac{1}{\sqrt{2}} ).
Step 2
2. Solve the quadratic equation.
Answer
Assuming that we want to solve for ( ax^2 + bx + c = 0 ) where we can rewrite it as follows:
[ ax^2 + bx + c = 0 ]
We can use the quadratic formula:
[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ]
This formula allows us to find the roots of the equation based on the coefficients ( a, b, \text{ and } c ).
Step 3
3. Analyze the solutions of the given quadratic in real numbers.
Answer
The analysis of the solutions can be carried out by determining the discriminant ( D = b^2 - 4ac ). If ( D > 0 ), we have two distinct real solutions. If ( D = 0 ), there is exactly one real solution, and if ( D < 0 ), there are no real solutions. This provides a comprehensive way to analyze the nature of the roots in the context of real numbers.