Question

Solve these


${x}^{2} - 5x + 6$
${x}^{2} - 11x + 28$
​

Answer 1

Answer:

hope this will help you more

Answer 2

Answer:

$x^2-5x+6$

x = 3, x = 2

$x^2-11x+28$

x = 7, x = 4

Step-by-step explanation:

One is asked to solve two quadratic equations. Both of these quadratic equations are in standard form. This means that the two equations follow the following general format;

$ax^2+bx+c$

The quadratic formula is a method of solving a quadratic equation using the coefficients of the terms in the equation. The quadratic equation is the following,

$\frac{-b(+-)\sqrt{b^2-4ac}}{2a}$

Substitute in each of the terms and solve for the roots in each equation;

$x^2-5x+6$

Substitute, and solve

$\frac{-(-5)(+-)\sqrt{(-5)^2-4(1)(6)}}{2(1)}\\\\=\frac{5(+-)\sqrt{25-25}}{2}$

$=\frac{5+1}{2}$          $=\frac{5-1}{2}$

$=3$               $=2$

$x^2-11x+28$

Substitute, and solve

$\frac{-(-11)(+-)\sqrt{(-11)^2-4(1)(28)}}{2(1)}\\=\frac{11(+-)\sqrt{121-112}}{2}$

$=\frac{11+\sqrt{9}}{2}$           $=\frac{11-\sqrt{9}}{2}$

$=\frac{11+3}{2}$              $=\frac{11-3}{2}$

$=7$                     $=4$