Question

Verify whether the given polynomial is zero of the polynomial , indicated against them
p ( x ) = 3x^2 − 1 , x = −1/√3, 2/√3.

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

x = - 1 / √3 is the zero of given equation.

x = 2 / √3 is not the zero of given equation.

Step-by-step-explanation:

The given quadratic expression is 3x² - 1.

The values given are x = - 1 / √3 and x = 2 / √3.

∴ 3x² - 1 = 0

By substituting x = - 1 / √3 in LHS of the above equation, we get,

→ 3 × ( - 1 / √3 )² - 1

→ 3 × ( 1 / 3 ) - 1

→ 1 - 1

→ 0

LHS = RHS

∴ x = - 1 / √3 is the zero of given equation.

Now, by substituting x = 2 / √3 in the LHS of given equation, we get,

3x² - 1

→ 3 × ( 2 / √3 )² - 1

→ 3 × ( 4 / 3 ) - 1

→ 4 - 1

→ 3

LHS ≠ RHS

∴ x = 2 / √3 is not the zero of given 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:

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