Question

2x²-2x-24=0
solve from quadratic Equations​

Answer 1

Answer:

-3 or 4

Step-by-step explanation:

2x²-2x-24 = 0

=> x²-x-12 = 0

=> x²-4x+3x-12 = 0

=> x(x-4) + 3(x-4) = 0

=> (x-4)(x+3) = 0

=> x = -3 or 4

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Answer 2

We recall the real roots of the given quadratic equation by the factorization method. Split the co-efficient of x  such that $b=p+q$ and $pq=ac$ of a quadratic equation $ax^2+bx+c=0$.

Given: $2x^2-2x-24=0$

Taking out 2 as common out from the equation,

$2(x^2-x-12)=0\\x^2-x-12=0$

Here $a=1,b=-1$ and $c=-12$

Using Middle term method,

  $b=p+q$

$-1=-4+3$

        $ac=pq$

$1\times-12=-4\times 3$

      $-12=-12$

Hence $p=-4,q=3$

           $x^2-x-12=0$

 $x^2-4x+3x-12=0$

$x(x-4)+3(x-4)=0$

        $(x-4)(x+3)=0$

$x-4=0$           $x+3=0$

     $x=4$                 $x=-3$