Question

Is x=-1,a zero of the polynomial x2-2x-1

Answer 1

$\rule{400}4$

▪︎ Given Polynomial:-

$\tt\leadsto {x}^{2} - 2x - 1$

▪︎ To Verify:-

• -1 is a zero of the given polynomial.

$\rule{400}2$

▪︎ Now,

• Let us find the zeroes of the given equation by factorization method:-

$\sf \mapsto {x}^{2} - ( 1 + 1)x - 1 = 0 \\ \\ \sf \mapsto {x}^{2} - x - x - 1 = 0 \\ \\ \sf \mapsto x(x - 1) + 1(x - 1) = 0 \\ \\ \sf \mapsto(x - 1)(x + 1) = 0 \\ \\ \sf \large\red{\fbox{\mapsto \: either \: \: x = 1 \: \: or \: \: x = - 1}}$

$\rule{400}2$

▪︎ Therefore we can conclude that -1 is a zero of the given polynomial.

$\rule{400}4$

Answer 2

Answer:

- 1 is not the zero of the given quadratic equation.

Step-by-step-explanation:

The given quadratic equation is x² - 2x - 1 = 0.

One of the zeroes of this quadratic equation is given as - 1.

We have to check whether - 1 is zero of the given quadratic equation or not.

By substituting x = - 1 in the LHS of the given quadratic equation, we get,

x² - 2x - 1 = 0

➞ ( - 1 )² - 2 × ( - 1 ) - 1

➞ 1 + 2 - 1

➞ 3 - 1

➞ 2

2 ≠ 0

∴ - 1 is not the zero of the given quadratic equation.

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:

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

5. Determininig the roots of the quadratic equation :

To determine the roots of the given quadratic equation, simply substitute the given values in place of the variable used and solve it.

If LHS = RHS then the given value is root of the given equation otherwise it's not the solution.