Find the value of a, if one root of the equation 2x² + ax + 8 = 0 is 1.

Form the quadratic equation whose roots are −4 and 3.

Find out the ratio of the sum and the product of two roots of the equation 7x² − 66x + 27 = 0.

If the sum of the roots of the equation ax² + bx + ac = 0 ( a ≠ 0) is zero, then find b.

If one root of the equation ax²+abcx+bc = 0 (a≠0) is reciprocal to the other, then (a) abc = 1 (b) b = ac (c) bc = 1 (d) a = bc

Under which condition the quadratic equation ax2 + bx + c = 0 (a ≠ 0) have one zero roots.

Number of solutions of equation x2 = x is (a) 1 (b) 2 (c) 0 (d) 3

Solve: + = 2, (x ≠ -3, 3)

If the roots of the equation x² − 22x + 105 = 0 are α and β, then find the value of 1/α + 1/β

Solve: = , x ≠ 0, -(a + b)

If the roots of a quadratic equation ax² + bx + c = 0 (a ≠ 0) are reciprocal and opposite in sign. Find (a + c)

Divide 16 into two parts in such a way that twice the square of the greater part is 164 more than the square of the smaller part