Ⅰ. 2x 2 + 11x + 12 = 0 Ⅱ. 5y 2 + 27y + 10 = 0

More Questions from Quadratic Equation

• Known root in a quadratic, find the other root and coefficient: Given 2x^2 + P x + 4 = 0 has a root x = 2. Find the second root and the value of P.
• Solve for roots in terms of parameters: Find the roots of 3a^2 x^2 − a b x − 2 b^2 = 0 in terms of a and b (assume a ≠ 0).
• Identify roots from coefficients: For ax^2 + (4a^2 − 3b)x − 12ab = 0 (a ≠ 0), choose the correct pair of roots.
• Express α^2 + β^2 in terms of a, b, c: If α and β are roots of ax^2 + bx + c = 0 (a ≠ 0), find α^2 + β^2.
• Find an equivalent equation to x^2 − 6x + 5 = 0 (same solution set): Choose the equation that has exactly the same set of real solutions as x^2 − 6x + 5 = 0.
• Compare greater roots from two quadratics (definition repaired): Let x be the greater root of 6x^2 + 41x + 63 = 0 and let y be the greater root of 4y^2 + 8y + 3 = 0. Choose the correct relation between x and y.
• Compare greater roots (definition repaired): Let x be the greater root of x^2 + 10x + 24 = 0 and y be the greater root of 4y^2 − 17y + 18 = 0. Choose the correct relation.
• Compare greater roots (definition repaired): Let x be the greater root of x^2 − 20x + 91 = 0 and y be the greater root of y^2 − 32y + 247 = 0. Choose the correct relation between x and y.
• Compare roots from two quadratics (set-based comparison, all cases): I) 3x^2 − 20x − 32 = 0 II) 2y^2 − 3y − 20 = 0 Based on all possible real roots of each equation, determine the correct relationship between x and y.
• Compare roots from two quadratics (check all combinations): I) 24x^2 + 38x + 15 = 0 II) 12y^2 + 28y + 15 = 0 Decide the correct relationship that always holds between any root x of I and any root y of II.

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