SOLUTION: Use the quadratic formula to determine, accurate to one decimal place, the roots, if they exist, for each quadratic relation. a) y = 2x2 + 3x + 1 b) y = x2 - 3x + 5

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Use the quadratic formula to determine, accurate to one decimal place, the roots, if they exist, for each quadratic relation. a) y = 2x2 + 3x + 1 b) y = x2 - 3x + 5       Log On


   

Question 1180546: Use the quadratic formula to determine, accurate to one decimal place, the roots, if they exist, for each quadratic relation.
a) y = 2x2 + 3x + 1
b) y = x2 - 3x + 5
c) y = x2 + x - 5
d) y = - 9x2 - 6x + 1
Found 2 solutions by mananth, MathLover1:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
2x2 + 3x + 1=0
comparing with ax^2 +bx +c =0
using the Quadratic Formula where
a = 2, b = 3, and c = 1
b^2-4ac= 9 + -8
b^2-4ac= 1
x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29
substitute the values in the formula

x1=( -3 + 1 )/ 4
x1= -0.5
x2=( -3 -1 ) / 4
x2= -1
Now you know thesteps
solve the rest of them


Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
a)
y+=+2x%5E2+%2B+3x+%2B+1
x+=+%28-b+%2B-sqrt%28b%5E2-4%2Aa%2Ac%29%29%2F%282%2Aa%29+...in your case a=2,b=3, and c=1
x+=%28-3%2B-sqrt%283%5E2-4%2A2%2A1%29%29%2F%282%2A2%29+
x+=+%28-3+%2B-+sqrt%28+9-8+%29%29%2F4+
x+=+%28-3+%2B-+sqrt%28+1+%29%29%2F4+
x+=+%28-3+%2B-+1%29%2F4+
solutions:
x+=+%28-3+%2B+1%29%2F4+=>x+=+-2%2F4+ =>x+=+-1%2F2+=>x+=+-0.5+
x+=+%28-3+-+1%29%2F4+=>x+=+-4%2F4+ =>x+=+-1

b)
+y+=+x%5E2+-+3x+%2B+5
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+...in your case a=1,b=-3, and c=5
x+=+%28-%28-3%29+%2B-+sqrt%28%28-3%29%5E2-4%2A1%2A5+%29%29%2F%282%2A1%29+
x+=+%283+%2B-+sqrt%289-20+%29%29%2F2+
x+=+%283+%2B-+sqrt%28-11+%29%29%2F2+
x+=+%283+%2B-+i%2Asqrt%2811+%29%29%2F2+
solutions:
x+=+3%2F2+%2B+i%2Asqrt%2811+%29%2F2+=>x+=1.5+%2B+1.7%2Ai
x+=+3%2F2+-+i%2Asqrt%2811+%29%2F2+=>x+=1.5+-+1.7%2Ai


c)
+y+=+x%5E2+%2B+x+-+5
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+...in your case a=1,b=1, and c=-5
x+=+%28-1+%2B-+sqrt%28+1%5E2-4%2A1%2A%28-5%29+%29%29%2F%282%2A1%29+
x+=+%28-1+%2B-+sqrt%28+1%2B20+%29%29%2F2+
x+=+%28-1+%2B-+sqrt%2821+%29%29%2F2+
x+=+%28-1+%2B-+4.6%29%2F2+

solutions:
x+=+%28-1+%2B+4.6%29%2F2+=> x=1.8
x+=+%28-1-+4.6%29%2F2+=> x=-2.8


d)
y+=+-9x%5E2+-+6x+%2B+1
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+...in your case a=-9,b=-6, and c=1
x+=+%28-%28-6%29+%2B-+sqrt%28+%28-6%29%5E2-4%2A%28-9%29%2A1+%29%29%2F%282%2A%28-9%29%29+
x+=+%286+%2B-+sqrt%28+36%2B36+%29%29%2F%28-18%29+
x+=+%286+%2B-+sqrt%282%2A36%29%29%2F%28-18%29+
x+=+%286+%2B-+6sqrt%282%29%29%2F%28-18%29+...simplify
x+=+%281+%2B-+1.4%29%2F%28-3%29+
solutions:

x+=+%281+%2B+1.4%29%2F%28-3%29+=>x=-0.8
x+=+%281+-+1.4%29%2F%28-3%29+=>x=+0.1