# If a and B are the roots of the equation 2x^2 - 3x + 4 = 0, how do you form the equation with roots a+2 and B+2?

Dec 8, 2016

$2 {X}^{2} - 11 X + 18 = 0$

#### Explanation:

$2 {x}^{2} - 3 x + 4 = 0$

let$\text{ "alpha,beta" }$ be the roots

$\alpha + \beta = - \frac{- 3}{2} = \frac{3}{2}$

$\alpha \beta = \frac{4}{2} = 2$

eqn with roots $\text{ "alpha+2," } \beta + 2$

let" "A=alpha+2; B=beta+2

$A + B = \alpha + 2 + \beta + 2 = \alpha + \beta + 4 = \frac{3}{2} + 4 = \frac{11}{2}$

$A B = \left(\alpha + 2\right) \left(\beta + 2\right) = \alpha \beta + 2 \alpha + 2 \beta = 4$

$A B = \alpha \beta + 2 \left(\alpha + \beta\right) + 4 = 2 + 2 \times \frac{3}{2} + 4 = 9$

new eqn.

${X}^{2} - \left(A + B\right) X + A B = 0$

${X}^{2} - \frac{11}{2} X + 9 = 0$

$2 {X}^{2} - 11 X + 18 = 0$