Find all numbers p for each of which the least value of the quadratic trinomial `4x^2-4px+p^2-2p+2` on the interval `0 le x le 2` is equal to 3

Find all numbers a for each of which the least value of the quadratic trinomial 4x^2 - 4ax + a^2 - 2a + 2 on the interva 0 le x le 2 is equal to 3.

For what values of p the quadratic equation 3x^(2) + 12x + 4p = 0 has equal roots?

Find values of p for which the quadratic polynomial 4x^(2) + px +3 has equal zeros .

Find the value of p for which the quadratic equation 4x^2+px+3=0 has equal roots

Find value of p for which the product of roots of the quadratic equation px^(2) +6x+ 4p =0 is equal to the sum of the roots.

The least value of the quadratic polynomial, f(x) = (2p^(2) + 1) x^(2) + 2 (4p^(2) - 1) x + 4(2p^(2)+1) for real values of p and x is