Math Problem Statement
(a^2-1)x^2+(a-1)x+(a^2-4a+3)=0 find a and x
Solution
To solve for and , let’s examine the quadratic equation:
This equation has two unknowns: and . We can approach this by examining conditions under which the quadratic has real roots. Here’s a step-by-step breakdown:
Step 1: Analyze the Quadratic in Terms of
The general form of a quadratic equation in is: where , , and .
Step 2: Apply the Discriminant Condition
For a quadratic equation to have real roots, its discriminant must be greater than or equal to zero: Plugging in the values for , , and , we get: Expanding this and setting will provide values for .
Step 3: Solve for
After solving for with , substitute the values of back into the original quadratic equation to find the values of .
Would you like a detailed expansion and solution for and substitution steps?
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Math Problem Analysis
Mathematical Concepts
Algebra
Quadratic Equations
Discriminant Analysis
Formulas
Quadratic equation Ax^2 + Bx + C = 0
Discriminant formula for real roots: Δ = B^2 - 4AC
Theorems
Discriminant condition for real roots
Suitable Grade Level
Grades 10-12
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