I need two numbers that multiply to get -20 and add to get 1. I'm doing a quadratic functions problem and I can't find the answer to this part of the question.It started out as finding the zero of the equation by factoring. The equation was g ( x ) = 2 x 2 + x − 10. I set it equal to zero, x 2 + x − 20 = 0. Now I have to factor but I can't find a way to. If it's prime, I don't know how to answer the main question. a × b = − 20 and a + b = 1

Question

I need two numbers that multiply to get -20 and add to get 1. I&#039;m doing a quadratic functions problem and I can&#039;t find the answer to this part of the question.It started out as finding the zero of the equation by factoring. The equation was   g  (  x  )  =  2      x    2    +  x  −  10. I set it equal to zero,       x    2    +  x  −  20  =  0. Now I have to factor but I can&#039;t find a way to. If it&#039;s prime, I don&#039;t know how to answer the main question.  a  ×  b  =  −  20 and   a  +  b  =  1

teleriasacr · Accepted Answer

Explanation:Since you know         a    +    b      and ab you also know the coefficients of the polynomial     (  x  −  a  )  (  x  −  b  )  =      x    2    −  (      a    +    b    )  x  +      a    b    ,  , so you can find the roots a, b by the quadratic formula.

Audrey Arnold · Accepted Answer

Step 1As Amzoti instructed in the comments, simply write down all the factors of 20 and one must give you what you desire, else the quadratic cannot be factored..  1  ×  20     either     1  +  20  ,  −  1  +  20  ,  1  +  −  20  ,  −  1  +  −  20      2  ×  10     either     2  +  10  ,  −  2  +  10  ,  2  +  −  10  ,  −  2  +  −  10      4  ×  5  ,     either     4  +  5  ,  −  4  +  5  ,  4  +  −  5  ,  −  4  +  −  5  It should be clear that the factors 1 and 20 and 2 and 10 will not give you 1. So let&#039;s focus on 4 and 5.  4  +  5  =  9    −  4  +  5  =  1    4  +  −  5  =  −  1    −  4  +  −  5  =  −  9Since -4,5 when added give you   b  =  1 and when multiplied give you −20, then g(x) factored is  g  (  x  )  =  2      x    2    +  x  −  10  =  (  x  −  4  )  (  x  +  5  )Alternately you can use the quadratic formula:  x  =            −      b      ±                        b          2                −        4        a        c                    2      a      You have   a  =  2, 1 and   c  =  −  10 so you can plug these respective values into the formula to get the values of x.

I need two numbers that multiply to get -20 and add to get 1. I'm doing a quadratic functions problem and I can't find the answer to this part of the question.

Answered question

Answer & Explanation

New Questions in Algebra I