Question-1 :- Solve x2 + 3 = 0.
Solution :-We have, x2 + 3 = 0 x2 = -3 x = ±√-3 = ±√3i
Question-2 :- Solve 2x2 + x + 1 = 0.
Solution :-We have, 2x2 + x + 1 = 0 Now, a = 2; b = 1; c = 1 b2 - 4ac = 12 - 4 x 2 x 1 = 1 - 8 = -7 Therefore, the solutions are given by x = (-1 ± √-7)/4 = (-1 ± √7i)/4
Question-3 :- Solve x2 + 3x + 9 = 0.
Solution :-We have, x2 + 3x + 9 = 0 Now, a = 1; b = 3; c = 9 b2 - 4ac = 32 - 4 x 1 x 9 = 9 - 36 = -27 Therefore, the solutions are given by x = (-3 ± √-27)/2 = (-3 ± 3√3i)/2
Question-4 :- Solve -x2 + x - 2 = 0.
Solution :-We have, -x2 + x - 2 = 0 Now, a = -1; b = 1; c = -2 b2 - 4ac = 12 - 4 x (-1) x (-2) = 1 - 8 = -7 Therefore, the solutions are given by x = (-1 ± √-7)/(-2) = (-1 ± √7i)/(-2)
Question-5 :- Solve x2 + 3x + 5 = 0.
Solution :-We have, x2 + 3x + 5 = 0 Now, a = 1; b = 3; c = 5 b2 - 4ac = 32 - 4 x 1 x 5 = 9 - 20 = -11 Therefore, the solutions are given by x = (-3 ± √-11)/2 = (-3 ± √11i)/2
Question-6 :- Solve x2 - x + 2 = 0.
Solution :-We have, x2 - x + 2 = 0 Now, a = 1; b = -1; c = 2 b2 - 4ac = (-1)2 - 4 x 1 x 2 = 1 - 8 = -7 Therefore, the solutions are given by x = (1 ± √-7)/2 = (1 ± √7i)/2
Question-7 :- Solve √2x2 + x + √2 = 0.
Solution :-We have, √2x2 + x + √2 = 0 Now, a = √2; b = 1; c = √2 b2 - 4ac = 12 - 4 x √2 x √2 = 1 - 8 = -7 Therefore, the solutions are given by x = (-1 ± √-7)/2√2 = (-1 ± √7i)/2√2
Question-8 :- Solve √3x2 - √2x + 3√3 = 0.
Solution :-We have, √3x2 - √2x + 3√3 = 0 Now, a = √3; b = -√2; c = 3√3 b2 - 4ac = (-√2)2 - 4 x √3 x 3√3 = 2 - 36 = -34 Therefore, the solutions are given by x = (√2 ± √-34)/2√3 = (√2 ± √34i)/2√3
Question-9 :- Solve x2 + x + 1/√2 = 0.
Solution :-We have, x2 + x + 1/√2 = 0 √2x2 + √2x + 1 = 0 Now, a = √2; b = √2; c = 1 b2 - 4ac = (√2)2 - 4 x √2 x 1 = 2 - 4√2 = -2(2√2 - 1) Therefore, the solutions are given by x = [-√2 ± √-2(2√2 - 1)]/2√2 = [-√2 ± √2√(2√2 - 1)i]/2√2 = [-1 ± √(2√2 - 1)i]/2
Question-10 :- Solve x2 + x/√2 + 1 = 0.
Solution :-We have, x2 + x/√2 + 1 = 0 √2x2 + x + √2 = 0 Now, a = √2; b = 1; c = √2 b2 - 4ac = 12 - 4 x √2 x √2 = 1 - 8 = -7 Therefore, the solutions are given by x = (-1 ± √-7)/2√2 = (-1 ± √7i)/2√2