Let integer ‘p’ be one of the roots of ax2 + 4x + 6 = 0 and integer ‘q’ be one of the roots of 2x2 – 7x + 3 = 0. If p = q2, then what is the value of ‘a’?

The roots of the cubic equation 2x3 – 8x2 + ax + 6 = 0 are m + n, 2m, m – n. The value of a is ______.

If α, β are roots of x2 – 3ax + a2 = 0, find the value(s) of a if α2 + β2 = 74 .

If α and β are the roots of the expression 2x2 + 8x + 7 = 0, write down the value of pα2 + β2 + 1

The integral value of a for which ax2 + ax + a = 2x2 - 3x - 6 has equal roots is 3 2 – 3 – 2

If the roots of x2 – px + 2 = 0 are equal, then the value of p is: