Quadratic equations 1

Algebra Level 2

the quadratic equation $x^{2}$ +2wx+9=4x has two equal roots.Find the possible values of w.

w=5 or w=-1 w=-1 w=1 or w=5 w=5

1 solution

X X
May 30, 2018

$x^2+(2w-4)x+9=0$ , $2w-4=6\space or\space -6,w=5\space or \space-1$

I have a doubt. Please clarify it .

How did you get 2w - 4 = 6 or - 6 ?

Ram Mohith - 3 years ago

$9=3^2$ or $(-3)^2$ ,so $x^2+(2w-4)x+9=(x+3)^2$ or $(x-3)^2$

X X - 3 years ago

Thanks for your explanation.

Ram Mohith - 3 years ago

X X might have done this way if roots are equal then the discriminant is 0. implying $b^2-4ac =0 \implies b= \pm \sqrt{4ac} = \pm 6$ .

Naren Bhandari - 3 years ago

Yes. It is the procedure X X followed

Ram Mohith - 3 years ago