Answer:
Real numbers = 39 and 9
Step-by-step explanation:
The standard form of a quadratic equation is ax² + bx + c = 0
Given the following data;
a = 1
b = -43
c = 306
Quadratic equation formula is;
[tex] x = \frac {-b \; \pm \sqrt {b^{2} - 4ac}}{2a} [/tex]
Substituting into the equation, we have;
[tex] x = \frac {-(-43) \; \pm \sqrt {43^{2} - 4*1*306}}{2*1} [/tex]
[tex] x = \frac {43 \pm \sqrt {1849 - 1224}}{2} [/tex]
[tex] x = \frac {43 \pm \sqrt {625}}{2} [/tex]
[tex] x = \frac {43 \pm 25}{2} [/tex]
[tex] x_{1} = \frac {43 + 25}{2} [/tex]
[tex] x_{1} = \frac {68}{2} [/tex]
[tex] x_{1} = 39 [/tex]
[tex] x_{2} = \frac {43 - 25}{2} [/tex]
[tex] x_{2} = \frac {18}{2} [/tex]
[tex] x_{2} = 9 [/tex]
Therefore, the two real numbers are 39 and 9.
The quadratic equation now becomes;
x² - 43x + 306 = (x - 39)(x - 9) = 0
