Quadratic Formula Help

Question

Use a=-2 and c=9 to write an equation so that ax^2-6x+c=0 has one real solution

^also:

^{use a=2 and c=4 to write an equation so that ax^2-8x+c=0 has two real solutions}

Answer 1

ax^2 -6x + c= 0

a=-2, c=9

to have one solution, the discriminant must = 0

b^2-4ac = 0

36 -4(-2)(9) = 0

36+72 = 108 which does not =0

It has 2 solutions, not one

to have two solutions the discriminant >0

UNLESS ,maybe you intended to write -b, instead of -6. b and 6 can look very similar

then

a=-2 c=9

b^2-4ac = b^2-4(-2)(9) = b^2+72 =0

b=+/-sqr(-72)

b=+/-6isqr2= about +/-8.484i

there is no real solution, just two imaginary solutions