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If x² + bx + b = 0 has two real and distinct roots, then the value of b can be
A 2-digit number is seven times the sum of its digits and two (2) more than 5 times the product of its digits. Find the number.
Find the value(s) of p for which the quadratic equation given as (p + 4) x² − (p + 1) x + 1 = 0 has real and equal roots. Also, find the roots of the equation(s) so obtained.
The value of 'a' for which ax² + x + a = 0 has equal and positive roots is :
Find the value(s) of 'k' so that the quadratic equation 4x² + kx + 1 = 0 has real and equal roots.
If 'α' and 'β', are the zeroes of the polynomial p(y) = y² − 5y + 3, then find the value of α⁴β³ + α³β⁴.
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