2.In quadratic equation ax2 + bx + c = 0, if discriminant is D= b2 - 4ac, then roots of the quadratic equation are (choose the correct alternative)

(1) Real and distinct, if D > 0

(2) Real and equal (i. e., repeated roots), if D = 0.

(3) Non-real (i. e. imaginary), if D< 0

(4) All of the above are correct

(2) Real and equal (i.e., repeated roots), if D = 0.

Step-by-step explanation:

.In a quadratic equation ax2 + bx + c = 0, if discriminant is D= b2 - 4ac, then roots of the quadratic equation are

Real and equal (i.e., repeated roots), if D = 0.

If the D > b² - 4ac then it's real and distinct.

let's solve your equation step-by-step.

4x+2=2x+12

step 1: subtract 2x from both sides.

4x+2−2x=2x+12−2x

2x+2=12

step 2: subtract 2 from both sides.

2x+2−2=12−2

2x=10

step 3: divide both sides by 2.

2x

2

=

10

2

x=5

step-by-step explanation:

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.