Question

If sum of the roots is 'p' & the sum of their squares is \[q^2/] , then the equation is ;-

Answer 1

\[Ans. x^2-px+(p^2-q^2)/2=0\]

Answer 2

weird. where's the question from? (what class I mean)

Answer 3

Let the roots be \(\alpha \) and \(\beta\).
Given : \(\alpha+ \beta = p \)
\(\alpha ^{2} + \beta ^{2} = q^{2} \)
\( (\alpha + \beta)^{2} = \alpha ^{2} + \beta ^{2} + 2 \alpha \beta\)
\(\Rightarrow p^{2} = q^{2} + 2 \alpha \beta\)
\(\Rightarrow \alpha \beta = (p^{2} - q^{2})/2\)

So, sum of roots = p, product of roots = \((p^{2}-q^{2})/2\). Hence the quadratic equation is
\(x^{2} - px + (p^{2} - q^{2})/2 = 0 \)

Answer 4

word

Answer 5

Thanx! @FoolAroundMath