Question

If alpha beta are the zeroes of p of x equal to x square - 5x+6 then find alpha+beta-3alpha beta​

Answer 1

$\huge\underline {\sf {Answer:}}$

$\underline {\bold {Given:}}$

• $p(x) = x^2- 5x + 6$
• $\alpha , \ \beta \ are \ the \ zeroes$

$\underline {\bold {Find:}}$

• $\alpha + \beta - 3 \alpha \beta$

$\underline {\bold {Solution:}}$

Finding the zeroes :

$\implies x^2 - 5x + 6 = 0$

$\implies x^2 -3x -2x+ 6 =0$

$\implies x(x -3) -2( x-3) = 0$

$\implies (x - 3)(x - 2) = 0$

$\implies x= 3 \ or \ x=2$

$\alpha = 3 ,\ \beta = 2$

Solving for the equation:

$\implies \alpha + \beta - 3 \alpha \beta \\ \implies 3 + 2 - 3(3 × 2) \\ \implies 5 - 18 \\ \implies -15$