Question

42 .
Find the quadratie ecuation
whose roots

P+q÷p and p+q÷q also find
the
nature of roots when p=2 and 3=q​

Answer 1

$\bold\red{\underline{\underline{Answer:}}}$

$\bold\green{\underline{\underline{Solution}}}$

Given :-

Roots of quadratic equations are p+q÷p and

p+q÷p

Given values of p and q is 2 and 3 respectively

Substituting there values

2+2÷(3) & 2+2÷(3)

$\bold{Roots \ are \frac{4}{3} \ and \frac{4}{3}}$

$let \: one \: root \: be \: \alpha \: and \: other \: be \: \beta$

$\bold{\alpha + \beta = \frac{4}{3}+\frac{4}{3}}$

$\bold{\alpha+\beta=\frac{8}{3}}$

And

$\bold{\alpha×\beta=\frac{4}{3}×\frac{4}{3}}$

$\bold{\alpha×\beta=\frac{16}{9}}$

Quatratic equation is

$\bold{x^{2}-(\alpha+\beta)x+(\alpha×\beta)=0}$

i.e.

$\bold{x^{2} - \frac{8x}{3}+ \frac{16}{9}=0}$

Roots of the quatratic equations are real and equal.

Reason:The roots are greater than zero.