(a-1)x²+ac+1 Ka Mann Ydi -3h Or Suniyke Ho To A.ka Mann Dho​

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Introduction

Algebraic Equations are a fundamental concept in mathematics, and solving them is a crucial skill for students and professionals alike. In this article, we will delve into the world of quadratic equations and explore a specific problem: (a-1)x²+ac+1 ka Mann Yadi -3h or suniyke ho to a.ka Mann Dho. We will break down the solution step by step, using clear and concise language to ensure that readers understand the concept.

Understanding the Problem

The problem statement is a quadratic equation in the form of (a-1)x²+ac+1. We are given that the discriminant (Mann) is -3h, and we need to find the value of 'a' when the equation is suniyke (simplified). To solve this problem, we need to recall the formula for the discriminant of a quadratic equation, which is b²-4ac.

Formula for Discriminant

The discriminant (D) of a quadratic equation ax²+bx+c is given by the formula:

D = b²-4ac

In our problem, the quadratic equation is (a-1)x²+ac+1, so we can substitute the values of a, b, and c into the formula:

D = (0)²-4(a-1)(ac+1)

Simplifying the Discriminant

Now, let's simplify the expression for the discriminant:

D = -4(a-1)(ac+1)

Given Condition

We are given that the discriminant (Mann) is -3h, so we can set up the equation:

-4(a-1)(ac+1) = -3h

Solving for 'a'

To solve for 'a', we need to isolate the variable 'a' on one side of the equation. Let's start by expanding the left-hand side of the equation:

-4(a-1)(ac+1) = -4a^2c - 4ac - 4ac - 4

Now, let's simplify the equation:

-4a^2c - 8ac - 4 = -3h

Rearranging the Equation

To make it easier to solve for 'a', let's rearrange the equation:

-4a^2c - 8ac + 3h - 4 = 0

Factoring the Quadratic

The equation is a quadratic in 'a', so we can try to factor it:

-4a^2c - 8ac + 3h - 4 = -(4ac+4)(a+c) + 3h - 4

Simplifying the Factored Form

Now, let's simplify the factored form:

-(4ac+4)(a+c) + 3h - 4 = -(4ac+4)(a+c) + 3h - 4

Solving for 'a'

To solve for 'a', we need to isolate the variable 'a' on one side of the equation. Let's start by adding 4ac+4 to both sides of the equation:

-(4ac+4)(a+c) = -3h + 4ac + 4

Dividing Both Sides

Now, let's divide both sides of the equation by -(4ac+4):

a+c = (-3h + 4ac + 4) / -(4ac+4)

Simplifying the Expression

Now, let's simplify the expression:

a+c = (4ac + 4 - 3h) / (4ac + 4)

Canceling Common Factors

We can cancel out the common factor (4ac+4) from the numerator and denominator:

a+c = (1 - 3h / (4ac + 4))

Solving for 'a'

To solve for 'a', we need to isolate the variable 'a' on one side of the equation. Let's start by subtracting 'c' from both sides of the equation:

a = (1 - 3h / (4ac + 4)) - c

Simplifying the Expression

Now, let's simplify the expression:

a = (1 - 3h / (4ac + 4)) - c

Conclusion

In this article, we have solved the problem (a-1)x²+ac+1 ka Mann Yadi -3h or suniyke ho to a.ka Mann Dho. We have used the formula for the discriminant of a quadratic equation and simplified the expression to find the value of 'a'. The final solution is a = (1 - 3h / (4ac + 4)) - c.

Final Answer

The final answer is a = (1 - 3h / (4ac + 4)) - c.

References

  • [1] Algebraic Equations, Wikipedia
  • [2] Quadratic Equations, Khan Academy
  • [3] Discriminant, Math Open Reference

Related Topics

  • Quadratic Equations
  • Algebraic Equations
  • Discriminant
  • Factoring Quadratics

Tags

  • Algebraic Equations
  • Quadratic Equations
  • Discriminant
  • Factoring Quadratics
  • Math
  • Mathematics
  • Algebra
  • Quadratic Formula
  • Discriminant Formula
  • Factoring Quadratics Formula

Introduction

In our previous article, we solved the problem (a-1)x²+ac+1 ka Mann Yadi -3h or suniyke ho to a.ka Mann Dho. We received many questions from readers who were struggling to understand the solution. In this article, we will answer some of the most frequently asked questions (FAQs) related to the problem.

Q1: What is the discriminant of a quadratic equation?

A1: The discriminant of a quadratic equation is a value that can be calculated from the coefficients of the equation. It is used to determine the nature of the roots of the equation. The formula for the discriminant is b²-4ac.

Q2: How do I calculate the discriminant of the given equation?

A2: To calculate the discriminant of the given equation (a-1)x²+ac+1, we need to substitute the values of a, b, and c into the formula. The discriminant is given by:

D = (0)²-4(a-1)(ac+1)

Q3: What is the given condition in the problem?

A3: The given condition in the problem is that the discriminant (Mann) is -3h.

Q4: How do I solve for 'a' in the equation?

A4: To solve for 'a', we need to isolate the variable 'a' on one side of the equation. We can do this by rearranging the equation and factoring it.

Q5: What is the final solution for 'a'?

A5: The final solution for 'a' is:

a = (1 - 3h / (4ac + 4)) - c

Q6: Can you explain the concept of factoring quadratics?

A6: Factoring quadratics is a technique used to simplify quadratic equations. It involves expressing the equation as a product of two binomials. In the case of the given equation, we can factor it as:

-(4ac+4)(a+c) + 3h - 4

Q7: How do I simplify the factored form of the equation?

A7: To simplify the factored form of the equation, we need to expand the product and combine like terms.

Q8: Can you provide more examples of quadratic equations?

A8: Yes, here are a few examples of quadratic equations:

  • x²+4x+4 = 0
  • x²-6x+9 = 0
  • x²+2x+1 = 0

Q9: How do I determine the nature of the roots of a quadratic equation?

A9: To determine the nature of the roots of a quadratic equation, we need to calculate the discriminant. If the discriminant is positive, the equation has two distinct real roots. If the discriminant is zero, the equation has one real root. If the discriminant is negative, the equation has no real roots.

Q10: Can you provide more resources for learning about quadratic equations?

A10: Yes, here are a few resources for learning about quadratic equations:

  • Khan Academy: Quadratic Equations
  • Math Open Reference: Quadratic Equations
  • Wikipedia: Quadratic Equation

Conclusion

In this article, we have answered some of the most frequently asked questions related to the problem (a-1)x²+ac+1 ka Mann Yadi -3h or suniyke ho to a.ka Mann Dho. We hope that this article has been helpful in clarifying any doubts that readers may have had.

Final Answer

The final answer is a = (1 - 3h / (4ac + 4)) - c.

References

  • [1] Algebraic Equations, Wikipedia
  • [2] Quadratic Equations, Khan Academy
  • [3] Discriminant, Math Open Reference

Related Topics

  • Quadratic Equations
  • Algebraic Equations
  • Discriminant
  • Factoring Quadratics
  • Math
  • Mathematics
  • Algebra
  • Quadratic Formula
  • Discriminant Formula
  • Factoring Quadratics Formula