Question

Find the zeroes of the polynomial

2x^2- 2x -8.
plz tell full step by step answer​

Answer 1

1. please mark it as brainliest

THANKS

Answer 2

Answer:

The roots of the given quadratic equation are

$\boxed{\red{\sf\:x\:=\:\dfrac{1\:\pm\:\sqrt{17}}{2}}}$

Step-by-step-explanation:

The given quadratic equation is

$\sf\:2x^{2}\:-\:2x\:-\:8\:=\:0$.

$\therefore\sf\:x^{2}\:-\:x\:-\:4\:=\:0\:\:\:[\:Dividing\:both\:sides\:by\:2\:]$

Comparing with $\sf\:ax^{2}\:+\:bx\:+\:c\:=\:0$, we get,

$\sf\:a\:=\:1\\\\\sf\:b\:=\:-\:1\\\\\sf\:c\:=\:-\:4$

Now, by using quadratic formula, we get,

$\boxed{\red{\sf\:x\:=\:\dfrac{-\:b\:\pm\:\sqrt{b^{2}\:-\:4ac}}{2a}}}\\\\\\\implies\sf\:x\:=\:\dfrac{-\:(\:-\:1\:)\:\pm\:\sqrt{(\:1\:)^{2}\:-\:4\:\times\:1\:\times\:(\:-\:4\:)}}{2\:\times\:1}\\\\\implies\sf\:x\:=\:\dfrac{1\:\pm\:\sqrt{1\:+\:16}}{2}\\\\\implies\boxed{\red{\sf\:x\:=\:\dfrac{1\:\pm\:\sqrt{17}}{2}}}$

Additional Information:

1. Quadratic Equation :

An equation having a degree '2' is called quadratic equation.

The general form of quadratic equation is

ax² + bx + c = 0

Where, a, b, c are real numbers and a ≠ 0.

2. Roots of Quadratic Equation:

The roots means nothing but the value of the variable given in the equation.

3. Methods of solving quadratic equation:

There are mainly three methods to solve or find the roots of the quadratic equation.

A) Factorization method

B) Completing square method

C) Formula method

4. Formula to solve quadratic equation:

$\boxed{\red{\sf\:x\:=\:\dfrac{-\:b\:\pm\:\sqrt{b^{2}\:-\:4ac}}{2a}}}$