Question

if p and q are the zeros of quadratic polynomial f(x)= ax^2 +bx +c then evaluate 1/p - 1/q.​

Answer 1

Answer:

√(b^2 - 4ac) /c

Step-by-step explanation:

ax^2 +bx +c =0

or, x^2 + (b/a) x +c/a=0

if p and q are zeros of quadretic polynomial

then, p+q = - b/a and pq = c/a

now, (p+q)^2 = b^2/a^2

or,( q-p)^2 +4pq = b^2/a^2

or,( q-p)^ =( b^2/a^2)- 4* c/a

or, (q-p)^2 = (b^2-4ac)/a^2

or, q-p = √(b^2-4ac)/a

therefore, 1/p - 1/q = (q-p)/pq

= √(b^2 -4ac) / a * c/a

= √(b^2-4ac)/c