Quadratic Equation Questions

• The roots of the equation ax 2 + ( 4a 2 - 3b )x - 12ab = 0 are
• If α and β are the roots of the equation ax 2 + bx + c = 0, find the value of α2 + β2
• An equation equivalent to the quadratic equation x2 − 6x + 5 = 0 is :
• Ⅰ. 6x2 + 41x + 63 = 0 Ⅱ. 4y2 + 8y + 3 = 0
• Ⅰ. x 2 + 10x + 24 = 0 Ⅱ. 4y 2 − 17y + 18 = 0
• Ⅰ. x 2 − 20x + 91= 0 Ⅱ. y 2 − 32y + 247= 0
• Ⅰ. 3x 2 − 20x −32 = 0 Ⅱ. 2y 2 − 3y − 20 = 0
• Ⅰ. 24x 2 + 38x + 15 = 0 Ⅱ.12y 2 + 28y + 15 = 0
• The value of k for which the roots α, β of the equation : x2 − 6x + k = 0 satisfy the relation 3α + 2β = 20, is
• The positive value of m for which the roots of the equation 12x2 + mx + 5 = 0 are in the ratio 3 : 2 is :
• If α, β are the roots of the equation x2 + kx + 12 = 0 such that α − β = 1, the value of k is
• Determine k such that the quadratic equation x2 - 2( 1 + 3k ) x + 7 ( 3 + 2k ) = 0 has equal roots.
• If α and β are the roots of the equation x2 - 3λx + λ2 = 0, find λ if α2 + β2 = 7 4
• If a and b are the roots of the equation x 2 - 6x + 6 = 0, find the value of 2(a 2 + b 2).
• If α and β be the roots of the equation ax 2 + bx + c = 0, find the value of α 2/β + β 2/α .
• If α and β are the roots of the equation x 2 - 11x + 24 = 0, find the equation having the roots α + 2 and β + 2
• If x 2 = 6 + √ 6 + √6 + √6 + .... ∞ , then what is one of the value of x equal to?
• If a = p / (p + q) and b = q / (p - q), then and ab/a + b is equal to
• The sum of the roots of the equation x 2 + px + q = 0 is equal to the sum of their squares, then
• If α and β are the roots of the equation 8x 2 - 3x + 27 = 0, find the value of (α 2/β) 1/3 + (β 2/α) 1/3