Answer:
[tex]a = p*q\\b = (p*s)+(q*r)\\c = r*s[/tex]
Step-by-step explanation:
We are given the standard form of trinomial
[tex]ax^2+bx+c[/tex]
After factorization, the form is:
[tex](px+r)(qx+s)[/tex]
We have to compare the factored form and the standard form to find the values of a,b and c in terms of p,q,r and s. For this purpose, the factored form will be converted into standard form.
Multiplying the both factors
[tex](px+r)(qx+s)\\=px(qx+s)+r(qx+s)\\= pqx^2+psx+qrx+rs\\= pqx^2+(ps+qr)x+rs[/tex]
Comparing both forms with each other
After comparing
[tex]a = pq = p*q\\b = ps+qr = (p*s)+(q*r)\\c = rs = r*s[/tex]
Hence,
[tex]a = p*q\\b = (p*s)+(q*r)\\c = r*s[/tex]
