Quadratic Equations

Answer

Step 1: Split the middle term so that p + q = -5 and p × q = 2 × 3 = 6. The pair is -2 and -3. Step 2: Rewrite: 2x^2 - 5x + 3 = 2x^2 - 2x - 3x + 3 Step 3: Group: = 2x(x - 1) - 3(x - 1) = (2x - 3)(x …

Answer

Step 1: Find two factors that split -x so that p + q = -1 and p × q = 6 × (-2) = -12. The pair is 3 and -4. Step 2: Rewrite: 6x^2 - x - 2 = 6x^2 + 3x - 4x - 2 Step 3: Group: = 3x(2x + 1) - 2(2x + 1)…

Answer

Step 1: Identify a, b, c. a = 3, b = -6, c = 2 Step 2: Use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a) Step 3: Substitute values: x = (6 ± √(36 - 24)) / 6 = (6 ± √12) / 6 = (6 ± 2√3) / 6 …

Answer

Step 1: Divide by 5: x^2 - (6/5)x - 2/5 = 0 Step 2: Move the constant term: x^2 - (6/5)x = 2/5 Step 3: Add the square of half the x-coefficient: Half of -6/5 is -3/5, so add (3/5)^2 = 9/25 to both s…

Answer

Step 1: Find the discriminant. D = b^2 - 4ac Here, a = 4, b = 3, c = 5 Step 2: Substitute: D = 3^2 - 4(4)(5) = 9 - 80 = -71 Step 3: Since D < 0, the equation has no real roots. Answer: No real root…

Answer

Step 1: Identify a, b, c. a = 2, b = -2√2, c = 1 Step 2: Find the discriminant. D = b^2 - 4ac = (-2√2)^2 - 4(2)(1) = 8 - 8 = 0 Step 3: D = 0 means two equal real roots. Step 4: Use the formula: x =…

Answer

Step 1: Multiply both sides by x: x^2 + 1 = 3x Step 2: Rearrange: x^2 - 3x + 1 = 0 Step 3: Use the quadratic formula: x = (3 ± √(9 - 4)) / 2 = (3 ± √5) / 2 Answer: Roots are (3 + √5)/2 and (3 - √5)…

Answer

Step 1: Multiply both sides by 6x: 6x^2 - 2 = x Step 2: Rearrange: 6x^2 - x - 2 = 0 Step 3: Factorise: 6x^2 - x - 2 = (3x - 2)(2x + 1) Step 4: Set factors equal to zero: 3x - 2 = 0 or 2x + 1 = 0 S…