Let be a positive integer

MATHEMATICS · Subjective · CBSE · Mathematics · Quadratic Equations · Quadratic Equations

Problem

Let

n

be a positive integer. Consider the quadratic equation

(n+2)x^{2}-2(2n-1)x+(n^{2}-4n+3)=0

. (i) Find all positive integers

n

for which the equation has equal real roots. (ii) For each value of

n

obtained in (i), compute the common root. (iii) Verify that the value of

n

obtained indeed keeps the coefficient of

x^{2}

non-zero.