QUADRATIC EQUATIONS( LECTURE 5 )

Quadratic Equations 

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Learning outcomes, covered so far:

1. recall general form of a quadratic equation

2. identify  any  given equation as quadratic .

3. form quadratic equations from word problems . 

4. solve quadratic equations by factorization method hence, the roots of the equation.
5. comprehend and translate the word problems as quadratic equations and solve them  using factorization method.
6. Comprehend quadratic formula

7. Apply quadratic formula to find roots of the quadratic equation

Today's learning outcome is:

I will be able to:
1. Reduce the given equation to a quadratic equation
2. Apply quadratic formula to find roots of the quadratic equation

                               

Please ➤

RECALL:

Can also be interpreted as:

Q1) Find the roots of the quadratic equation using the quadratic formula:

x + 1/x = 3, x ≠ 0

A1) x + 1/x = 3    {Given}

     ⇒  (x² + 1)/x = 3  {Take LCM}

     ⇒  (x² + 1) = 3x  {Take x to RHS numerator & multiply}

     ⇒  x² + 1 - 3x = 0  {Take 3x to RHS}

     ⇒  x² - 3x + 1 = 0  {Rearrange}

Step-1: a = ___ , b = ____ , c =____

        {Hint: Coefficients x² , x & constant}

Step-2: d = (__) - 4(__)(__) = ____

        {Hint: Coefficients x² , x & constant}

Step-3: if d < 0 then , Answer = "No Real Roots" , else got to STEP-4

Step-4: α = {-(__) + √__} / 2(__)  = ____

             β = {-(__) - √__} / 2(__)  = ____

                          {Hint: input the values of b, d and a in that order for both α & β, refer to

the formula in the picture give above}

Q2) Find the roots of the quadratic equation using the quadratic formula:

1/x - 1/(x-2) = 3, x ≠ 0,2

A2) 1/x + 1/(x-2) = 3    {Given}

     ⇒  (x - 2 + x)/x(x-2) = 3  {Take LCM}

     ⇒  (2x - 2) = 3x(x - 2)  {Take x to RHS numerator & multiply}

     ⇒  2x - 2 = 3x² - 6x  {simplify RHS

     ⇒  x² - 8x + 2 = 0  {Rearrange}

Step-1: a = ___ , b = ____ , c =____

        {Hint: Coefficients x² , x & constant}

Step-2: d = (__) - 4(__)(__) = ____

        {Hint: Coefficients x² , x & constant}

Step-3: if d < 0 then , Answer = "No Real Roots" , else got to STEP-4

Step-4: α = {-(__) + √__} / 2(__)  = ____

             β = {-(__) - √__} / 2(__)  = ____

                          {Hint: input the values of b, d and a in that order for both α & β, refer to

the formula in the picture give above}

REFLECTION: 
You learnt this word "caveat" yesterday.
The lock down due to Covid-19

has been a boon to the nature,

as the nature is 

in the self healing process.

This has given us 

a caveat

to be responsible 

in our actions towards nature

Please read about SDG-17

HOME WORK:

Ex. 4.3 Q3 + Quadratic Eq-2 assignment sent (please access through your student login on redox app or school website)

Take Care & keep smiling