Question

If the ratio of the roots of the eq. \[x^{2}+bx+c=0\]is same as that of \[x^{2}+qx+r=0\], then show that \[b^{2}r=q^{2}c\]

Answer 1

I think you should first use the formula for sum of roots and products of roots..

Answer 2

your sol. would be more helpful

Answer 3

notica that \(\huge \frac{x_{1}}{x_{2}}+\frac{x_{2}}{x_{1}}=\frac{x_{1}^2+x_{2}^2}{x_{1}x_{2}}=\frac{(x_{1}+x_{2})^2}{x_{1}x_{2}}-2 \)

Answer 4

how both eq. have common roots?

Answer 5

If the ratio of the roots of the 2 equations are equal then x1/x2+x2/x1 will be equal also for 2 equations

Answer 6

x1/x2+x2/x1 for equation 1 : \(\huge \frac{b^2}{c}-2 \)

x1/x2+x2/x1 for equation 2 : \(\huge \frac{q^2}{r}-2 \)

Answer 7

so b^2 r= q^2 c