Question

7. In a quadratic equation
ax2+bx+c 0.if acab then the roots
are
1.-a.1
2.a, 1
3. -1, c/a
4.1,c/a​

Answer 1

In the equation ax^2+bx+c = 0, the roots are

x1 = [-b+(b^2–4ac)^0.5]/2a and

x2 = [-b-(b^2–4ac)^0.5]/2a

If the roots are to be equal, then x1 = x2, or

[-b+(b^2–4ac)^0.5]/2a = [-b-(b^2–4ac)^0.5]/2a, or

+(b^2–4ac)^0.5] =-(b^2–4ac)^0.5, or

2(b^2–4ac) = 0, or

b^2 = 4ac, or

b = 2(ac)^0.5.

So the equation will have equal roots when b = 2(ac)^0.5. And, the equation becomes

ax^2+2(ac)^0.5 x+c = 0 and the two equal roots will be

x3=[-2(ac)^0.5 +(4ac-4ac)^0.5]/2a or

x3=x4 = -(c/a)^0.5

The equal roots will be x = -(c/a)^0.5, when b = 2(ac)^0.5.

hope this helps u