Find the roots of the quadratic equation 9x²-3x-20
Answers
Step-by-step explanation:
ges made to your input should not affect the solution:
(1): "x2" was replaced by "x^2".
STEP
1
:
Equation at the end of step 1
(32x2 - 3x) - 20
STEP
2
:
Trying to factor by splitting the middle term
2.1 Factoring 9x2-3x-20
The first term is, 9x2 its coefficient is 9 .
The middle term is, -3x its coefficient is -3 .
The last term, "the constant", is -20
Step-1 : Multiply the coefficient of the first term by the constant 9 • -20 = -180
Step-2 : Find two factors of -180 whose sum equals the coefficient of the middle term, which is -3 .
-180 + 1 = -179
-90 + 2 = -88
-60 + 3 = -57
-45 + 4 = -41
-36 + 5 = -31
-30 + 6 = -24
-20 + 9 = -11
-18 + 10 = -8
-15 + 12 = -3 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -15 and 12
9x2 - 15x + 12x - 20
Step-4 : Add up the first 2 terms, pulling out like factors :
3x • (3x-5)
Add up the last 2 terms, pulling out common factors :
4 • (3x-5)
Step-5 : Add up the four terms of step 4 :
(3x+4) • (3x-5)
Which is the desired factorization
Final result :
(3x - 5) • (3x + 4)