determine the set of values of p for which the given quadratic equation has real roots (i) 5x^2-2px+3=0

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Let P, Q, R, S and T are five sets about the quadratic equation

(a – 5) $x^{2}$ – 2ax + (a – 4) = 0, a $\neq$ 5 such that

P : All values of ‘a’ for which the product of roots of given quadratic equation is positive.

Q : All values of ‘a’ for which the product of roots of given quadratic equation is negative.

R : All values of ‘a’ for which the product of real roots of given quadratic equation is positive.

S : All values of ‘a’ for which the roots of given quadratic are real.

T : All values of ‘a’ for which the given quadratic equation has complex roots.

Which statement is correct regarding sets, P, Q and R ?

Let P, Q, R, S and T are five sets about the quadratic equation
(a – 5) $x^{2}$ – 2ax + (a – 4) = 0, a $\neq$ 5 such that
P : All values of ‘a’ for which the product of roots of given quadratic equation is positive.
Q : All values of ‘a’ for which the product of roots of given quadratic equation is negative.
R : All values of ‘a’ for which the product of real roots of given quadratic equation is positive.
S : All values of ‘a’ for which the roots of given quadratic are real.
T : All values of ‘a’ for which the given quadratic equation has complex roots.

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