value of the roots of the quadratic equation,x^2-x-6=0 are _____.
Answers
Answer:
x=2 x=-3
Step-by-step explanation:
Factoring x2-x-6
The first term is, x2 its coefficient is 1 .
The middle term is, -x its coefficient is -1 .
The last term, "the constant", is -6
Step-1 : Multiply the coefficient of the first term by the constant 1 • -6 = -6
Step-2 : Find two factors of -6 whose sum equals the coefficient of the middle term, which is -1 .
-6 + 1 = -5
-3 + 2 = -1 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -3 and 2
x2 - 3x + 2x - 6
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 :
2 • (x-3)
Step-5 : Add up the four terms of step 4 :
(x+2) • (x-3)
Which is the desired factorization
Equation at the end of step 1 :
(x + 2) • (x - 3) = 0