Question

1. 5x² - 13x + 6 = 0

Explanation:

Step1: Factor the quadratic trinomial

We need two numbers that multiply to $5\times6=30$ and add to $-13$. These numbers are $-10$ and $-3$. Split the middle term:
$5x^2 -10x -3x +6=0$
Group and factor:
$5x(x-2)-3(x-2)=0$
$(5x-3)(x-2)=0$

Step2: Solve for $x$ using zero product property

Set each factor equal to 0:

1. $5x-3=0$
2. $x-2=0$

Solve first equation:
$5x=3 \implies x=\frac{3}{5}$

Solve second equation:
$x=2$

Answer:

$x=\frac{3}{5}$ or $x=2$