Question

the following equation are the root of the quadratic equation ( x)×2-9x+20= 0 by completing square method?​

Answer 1

Step-by-step explanation:

Method 1: A quadratic equation is of the form ax^2+bx+c = 0

See if b can be written as a sum or difference of ac.

Here b = 9, and ac = 20 = 4x5

Given that x^2+9x+20 = 0

break up the coefficient of x and write the equation as

x^2+4x+5x+20 = 0

Make pairs of terms and take out the like terms as

x(x+4) + 5(x+4) = 0, then the factors to get

(x+4)(x+5) = 0. From this we conclude

So x = -4 or -5. Answer.

Method 2: A quadratic equation is of the form ax^2+bx+c = 0

x1 = [-b+(b^2–4ac)^0.5]/2

x2 = [-b- (b^2–4ac)^0.5]/2

Applying it in this equation: x^2+9x+20 = 0

x1 = [-9+(9^2 -4*1*20)^0.5]/2

= [-9+(81–80)^0.5]/2

= [-9+1]/2

= [-8]/2 = -4

x2 = [-9-(9^2 -4*1*20)^0.5]/2

= [-9-(81–80)^0.5]/2

= [-9-1]/2

= [-10]/2 = -5.

x= -4 or -5. Answer.