Maths-
General
Easy

Question

What are the solutions of the quadratic equation 4 x squared minus 8 x minus 12 equals 0 ?

  1. x equals negative 1 text  and  end text x equals negative 3
  2. x = -1 and x = 3
  3. x = 1 and x = -3
  4. x = 1 and x = 3  

Hint:

Hint:- 
The word "quadratic" is originated from the word "quad" and its meaning is "square". It means the quadratic equation has a variable raised to 2 as the greatest power term. The standard form of a quadratic equation is given by the equation ax2 + bx + c = 0, where a ≠ 0. We know that any value(s) of x that satisfies the equation is known as a solution (or) root of the equation and the process of finding the values of x which satisfies the equation ax2 + bx + c = 0 is known as solving quadratic equations.

The correct answer is: x = -1 and x = 3



    • The given equation is 4x2-8x-12=0.
    • We can see 4 is the like factor of all terms in the equation . So we can write the equation as
    4 (x2- 2x - 3 )= 0
    Factoring  x2 - 2x - 3
    The first term is,  x2  its coefficient is  1 .
    The middle term is, -2x  its coefficient is  -2 .
    The last term i.e. constant is  -3 

    Step-1 : Multiply the coefficient of the first term by the constant   1 × (-3) = -3 

    Step-2 : Find two factors of  -3  whose sum equals the coefficient of the middle term, which is  -2 .
    -3   +  1   = -2
    Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -3  and  1
    x2 - 3x + 1x - 3

    Step-4 : Add up the first 2 terms, pulling out like factors :
    x • (x-3)
    Add up the last 2 terms, pulling out common factors :
    1 • (x-3)
    Step-5 : Add up the four terms of step 4 :
    (x+1)  •  (x-3)
    Which is the desired factorization
    • So, the equation becomes  
    4  (x + 1)  (x - 3)  = 0
    • A product of several terms equals zero. When a product of two or more terms equals zero, then at least one of the terms must be zero. 
    We shall now solve each term = 0 separately . In other words, we are going to solve as many equations as there are terms in the product
    Any solution of term = 0 solves product = 0 as well.
    Solve :    4   =  0
    This equation has no solution.
    A a non-zero constant never equals zero.
    Solve  :    x+1 = 0
    Subtract  1  from both sides of the equation : 
    x = -1
    Solve  : x - 3 = 0
    Add 3  to both sides of the equation : 
    x = 3
    • Therefore, we get the roots of the equation as x = -1 and x = 3.
    Note:-There are different ways of solving quadratic equations.
    • Solving quadratic equations by factoring
    • Solving quadratic equations by completing the square
    • Solving quadratic equations by graphing
    • Solving quadratic equations by quadratic formula
    But most popular method is solving quadratic equations by factoring.

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