SOLUTION: 1. Given the following polynomial: 2x^2 + 7x - 15 = 0 Check all that apply.  The value of the discriminant is 169.  There are 2 real roots.  There ar

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: 1. Given the following polynomial: 2x^2 + 7x - 15 = 0 Check all that apply.  The value of the discriminant is 169.  There are 2 real roots.  There ar      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


   



Question 1085653: 1. Given the following polynomial: 2x^2 + 7x - 15 = 0 Check all that apply.
 The value of the discriminant is 169.
 There are 2 real roots.
 There are 2 irrational roots.
 The graph intersects the y-axis twice.
 The parabola is directed upward.
 The axis of symmetry is located at: x = -7/4
 The vertex is located at: (-7/4, -49/8)
 The roots are: {5,3/2}
 The graph intersects the y axis at (0, -15).
 The graph intersects the x-axis at (-5, 0) and (1.5, 0)





II.
Use the quadratic formula to solve the following: 3x^2 - x + 2 = 0

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

I. Given the following polynomial:
2x%5E2+%2B+7x+-+15+=+0+
Check all that apply.
b%5E2-4ac=7%5E2-4%2A2%28-15%29=49%2B120=169
 The value of the discriminant is 169.
 There are 2+real roots.
discriminant%3E0, so there are 2 real roots
 The parabola is directed upward.
since a=2 which is positive number, the parabola+is directed upward
 The axis of symmetry is located at: x+=+-7%2F4
2+%28x+%2B+7%2F4%29%5E2+-+169%2F8+=+0-> h=-7%2F4->the axis of symmetry goes through vertex (-7%2F4,-+169%2F8) and it is a vertical line x+=+-7%2F4

 The graph intersects the y axis at (0,+-15).
y=2x%5E2+%2B+7x+-+15+
y=2%2A0%5E2+%2B+7x%2A+-+15
y=-15
 The graph intersects the x-axis at (-5, 0) and (1.5,+0)
%28x+%2B+5%29+%282+x+-+3%29+=+0
%28x+%2B+5%29++=+0 -> x=-5 -> point (-5, 0)
%282+x+-+3%29+=+0+-> x=3%2F2=1.5+-> (1.5,+0)

+graph%28+600%2C+600%2C+-10%2C+10%2C+-20%2C+10%2C+2x%5E2+%2B+7x+-+15%29+

II.
Use the quadratic formula to solve the following:
3x%5E2+-+x+%2B+2+=+0+
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-%28-1%29+%2B-+sqrt%28+%28-1%29%5E2-4%2A3%2A2+%29%29%2F%282%2A3%29+
x+=+%281+%2B-+sqrt%281-24+%29%29%2F6+
x+=+%281+%2B-+sqrt%28-23+%29%29%2F6+
x+=+%281+%2B-+i%2Asqrt%2823+%29%29%2F6+
solutions:
x+=+%281%2F6%29%281+%2B+i%2Asqrt%2823+%29%29+
x+=+%281%2F6%29%281+-+i%2Asqrt%2823+%29%29+