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

1.	Let P, Q, R, S and T are five sets about the quadratic equation (a – 5)x2 – 2ax + (a – 4) = 0, a ≠ 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 ?
Answer» 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)x2 – 2ax + (a – 4) = 0, a ≠ 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 ?

Answer»

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 ?