Now, we group the terms and factor out the common factors from each pair. From the first two terms, 2x² - 2x, we factor out 2x, leaving x-1. From the last two terms, -3x + 3, we factor out -3, also leaving x-1.

Now, we group the terms and factor out the common factors from each pair. From the first two terms, 2x² - 2x, we factor out 2x, leaving x-1. From the last two terms, -3x + 3, we factor out -3, also leaving x-1.

Find the roots of the equation $2x^2 - 5x + 3 = 0$ by factorisation.

Answer: The roots of the equation are $x = 1$ and $x = \frac{3}{2}$ .

Step-by-step solution

Step 1: Identify coefficients and split the middle term

To factorize a quadratic equation of the form $ax^2 + bx + c = 0$ , we need to find two numbers whose product is $ac$ and whose sum is $b$ . Here, $a=2$ , $b=-5$ , and $c=3$ . So, we need two numbers whose product is $2 \times 3 = 6$ and whose sum is $-5$ . These numbers are $-2$ and $-3$ . We then split the middle term, $-5x$ , into $-2x - 3x$ .

Step 2: Factor by grouping

Now, we group the terms and factor out the common factors from each pair. From the first two terms, $2x^2 - 2x$ , we factor out $2x$ , leaving $x-1$ . From the last two terms, $-3x + 3$ , we factor out $-3$ , also leaving $x-1$ .

Step 3: Factor the common binomial

Since $(x-1)$ is a common factor in both terms, we can factor it out, which gives us the product of two binomials: $(x-1)(2x-3) = 0$ .

Step 4: Solve for x

For the product of two factors to be zero, at least one of the factors must be zero. So, we set each factor equal to zero and solve for $x$ . This gives us the two roots of the quadratic equation.

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Find the roots of the equation 2x2−5x+3=02x^2 - 5x + 3 = 02x2−5x+3=0 by factorisation.