Question

Write quadratic equation if α + β = 7 and α × β = 10.

Answer 1

Question:

Write quadratic equation if α + β = 7 and α × β = 10.

Solution:

Given,

$\alpha + \beta = 7 - - - (i) \\ \alpha \times \beta = 10 - - - (ii)$

Substituting the value of a from eq i in eq.ii,we get

In terms of beeta we get

$\alpha = 7 - \beta - - i$

$(7 - \beta ) \beta = 10 - - ii \\ = > 7 \beta - { \beta }^{2} = 10 \\ = > 7 \beta - { \beta }^{2} - 10 = 0 \\ = > - { \beta }^{2} + 7 \beta - 10 = 0$

Again ,

In terms of Alpha we get,

$\beta = 7 - \alpha - - i$

Substituting The value of Alpha in eq ii we get,

$\alpha (7 - \alpha ) = 7 \\ = > 7 \alpha - { \alpha }^{2} = 7 \\ = > - { \alpha }^{2} - 7 \alpha - 7 = 0$

Therefore the two equations that we get are :

$- { \alpha }^{2} - 7 \alpha - 7 = 0 - - - - i \\ - { \beta }^{2} + 7 \beta + 10 = 0 - - - ii$