Question

find the zero of the polinomial x2-5x+3

Answer 1

Comparing the given polynomial with ax² + bx + c = 0

a=1, b=-5 and c=3

D= b²-4ac

=(-5)²-4(1)(3)

=25-12

=13

Here, D>0

Therefore, the given polynomial has two distinct real roots.

Using Quadratic Formula

$x = \frac{ - b ± \sqrt{D} }{2a} \\ x = \frac{5 ± \sqrt{13} }{2 \times 1} \\ x = \frac{5 ± \sqrt{13} }{2} \\ x = \frac{5 + \sqrt{13} }{2} ,\frac{5 - \sqrt{13} }{2}$