Question

5. Find the product of the roots of quadratic equation 2x2 +7x -4 = 0

Answer 1

Tip

To solve these type of question, we can use three different methods to solve a quadratic equation.

• Factorization method
• Completing the square method
• Quadratic formula

Step - 1

$2x^2 + 7x - 4 = 0$

Let's solve this equation by factorization method.

$2x^2 + 8x - x - 4 = 0$

According to sum - product pattern, the middle term can be split as $8x - x$.

Step - 2

Take $2x$ and $-1$ as common factors from the two pairs.

$2x(x + 4) -1(x + 4) = 0$

Step - 3

Write the equation in factorized form and find the roots.

$(2x - 1)(x + 4) = 0$

$2x - 1 = 0 \: and \: x + 4 = 0$

$2x = 1 \: and \: x = -4$

$\boxed{x = \dfrac{1}{2} \: and \: x = -4}$

Step - 4

We have found the roots of the given equation. According to the question, we need to find the product of the roots. Let's find it:

$= \dfrac{1}{2} \times -4$

$\underline{= -2}$

Final Answer

The product of the roots of the quadratic equation $2x^2 + 7x - 4 = 0$ is $-2$.