Question

How do you factor $5{x^2} - 7x + 2 = 0$ ?

Answer 1

Hint:In the given question, we have to find the factors of the given equation. The equation given in the question has a degree equal to 2 so it is quadratic. The standard form of a quadratic equation is $a{x^2} + bx + c = 0$ .
To find the factors of the given equation, we compare the given equation and the standard equation and get the values of a, b and c.
Then we will try to write b as a sum of two numbers such that their product is equal to the product of a and c, that is, ${b_1} \times {b_2} = a \times c$ , this method is known as factorization. We find the value of ${b_1}$ and ${b_2}$ by hit and trial.]
We move to some other methods like quadratic formula, graphing, and completing the
square method, if we are not able to solve an equation by factorization. Using this information, we can factor the given equation.

Complete step by step answer:
The given equation is $5{x^2} - 7x + 2 = 0$
We solve the given equation by factorization as follows –
$
5{x^2} - 7x + 2 = 0 \\
\Rightarrow 5{x^2} - 5x - 2x + 2 = 0 \\
\Rightarrow 5x(x - 1) + 2(x - 1) = 0 \\
\Rightarrow (5x + 2)(x - 1) = 0 \\
\Rightarrow 5x + 2 = 0,\,x - 1 = 0 \\
\Rightarrow x = \dfrac{{ - 2}}{5},\,x = 1 \\
$
Hence, the factors of the equation are $x + \dfrac{2}{5} = 0$ and $x - 1 = 0$ .

Note: A quadratic equation is a kind of polynomial equation. Factors/roots/solutions/zeros of the equation are the values of the unknown variable at which the function comes out to be zero. They are simply the x-intercepts as the value of y is zero at the x-axis. With the help of several methods like factorization, completing the square, quadratic formula, etc., the factors of a quadratic equation can be found easily.