Question:

Find the roots of the quadratic equation 2x^2+5x+3=0 by the method of completing the square.

Answer:

Step 1: Rewrite the equation in the form of ax^2+bx+c=0, where a, b, and c are constants.

2x^2+5x+3=0

Step 2: Divide each term by a (in this case, a = 2).

x^2 + (5/2)x + (3/2) = 0

Step 3: Rewrite the equation in the form of (x + h)^2 + k = 0.

(x + (5/4))^2 + (3/4) = 0

Step 4: Find the value of h.

h = (5/4)

Step 5: Find the value of k.

k = (3/4)

Step 6: Find the two roots of the equation.

x = -(5/4) ± √(-(3/4))

x = -(5/4) ± √(3/4)

Question:

x^2+x−2

Answer:

Step 1: Factor the expression.

(x - 2)(x + 1)

Step 2: Set each factor equal to zero.

x - 2 = 0 x + 1 = 0

Step 3: Solve each equation.

x = 2 x = -1

Question:

Solve : √2x^2+x+√2=0

Answer:

Step 1: Square both sides to get rid of the square root. 2x^2 + x + 2 = 0

Step 2: Rewrite the equation in standard form. 2x^2 + x - 2 = 0

Step 3: Factor the equation. (2x + 1)(x - 2) = 0

Step 4: Set each factor equal to zero and solve for x. 2x + 1 = 0 x = -1/2

x - 2 = 0 x = 2

The solutions are x = -1/2 and x = 2.

Question:

Solve : x^2+x+1​/√2=0

Answer:

Step 1: Multiply both sides of the equation by √2

x^2 + x + 1 = 0 * √2

Step 2: Simplify the left side of the equation

2x^2 + 2x + 2 = 0

Step 3: Factor the left side of the equation

2(x^2 + x + 1) = 0

Step 4: Set each factor equal to 0 and solve for x

2 = 0 OR x^2 + x + 1 = 0

Step 5: Since 2 does not equal 0, solve for x in the second equation

x^2 + x + 1 = 0

x = [-1 ± √(-1^2 - 4(1)(1))] / 2

x = [-1 ± √(-1 - 4)] / 2

x = [-1 ± √(-5)] / 2

x = [-1 ± √5] / 2

x = [-1 ± 2.236] / 2

x = -1.618 or -0.382

Question:

Solve : x2+x​/√2+1=0

Answer:

Step 1: Subtract 1 from both sides of the equation to get x2 + x/√2 = -1.

Step 2: Square both sides of the equation to get x2 + 2x + 1/2 = -1.

Step 3: Subtract 1/2 from both sides of the equation to get x2 + 2x = -3/2.

Step 4: Divide both sides of the equation by 2 to get x2 + x = -3/4.

Step 5: Subtract x from both sides of the equation to get x2 = -3/4 - x.

Step 6: Rewrite the equation in standard form to get x2 + x + (3/4) = 0.

Step 7: Factor the equation to get (x + (3/8))(x + (3/8)) = 0.

Step 8: Set each factor equal to 0 and solve for x to get x = -3/8.

Question:

For the quadratic equation x^2−2x+1=0, the value of x+1​/x is : A −1 B 1 C 2 D −2

Answer:

Step 1: Rearrange the equation to get x^2 - 2x + 1 = 0

Step 2: Factor the equation to get (x - 1)(x - 1) = 0

Step 3: Set each factor equal to 0 and solve for x: x - 1 = 0 –> x = 1

Step 4: Substitute x = 1 into x + 1/x to get 1 + 1/1 = 2

Answer: C 2

Question:

Solve the equation x^2+3x+5=0 for x.

Answer:

1. First, subtract 5 from both sides of the equation to isolate the x terms: x^2+3x=-5.

2. Next, factor the left side of the equation: x(x+3)= -5.

3. Divide both sides of the equation by (x+3) to isolate the x term: x=-5/(x+3).

4. To solve for x, set the denominator to 0 and solve for x: 0=x+3, x=-3.

5. Therefore, the solutions to the equation x^2+3x+5=0 are x=-3 and x=-5/(x+3).

Question:

Solve : √3x^2−√2x+3√3=0

Answer:

Step 1: Square both sides of the equation: 3x^2 - 2x√3 + 9 = 0

Step 2: Rewrite the equation as a quadratic equation: 3x^2 - 2x√3 + 9 = 0 3x^2 - 2x√3 + 9 - 9 = 0 - 9 3x^2 - 2x√3 = -9

Step 3: Factor the equation: 3x^2 - 2x√3 = -9 3x(x - √3) = -9

Step 4: Divide both sides of the equation by 3: 3x(x - √3) = -9 (x - √3) = -3

Step 5: Solve for x: (x - √3) = -3 x - √3 = -3 x = -3 + √3

The solution to the equation is x = -3 + √3.

Question:

Solve following equation : x^2+3=0 A ±3 B ±3 ​C ±i3 ​D ±3i

Answer:

Answer: C ±i3

Question:

If α and β are the roots of the quadratic equation x^2−3x−2=0 then α​/β+β​/α A 3​/2 B −3​/2 C 13​/2 D −13/2

Answer:

Step 1: Given equation is x^2−3x−2=0

Step 2: By using the quadratic formula, the roots of the equation can be determined.

α=(3+√17)/2

β=(3-√17)/2

Step 3: α​/β+β​/α= (3+√17)/2 / (3-√17)/2 + (3-√17)/2 / (3+√17)/2

Step 4: Simplifying, α​/β+β​/α= (3+√17)/(3-√17)+ (3-√17)/(3+√17)

Step 5: α​/β+β​/α= (3+√17 + 3-√17)/(3-√17)(3+√17)

Step 6: α​/β+β​/α= 6/(17-17)

Step 7: α​/β+β​/α= 6/0

Step 8: Since the denominator is 0, the answer is undefined.