Math, asked by simrankaurnagi8685, 1 month ago

If a, B are the zeroes of the polynomial 2x²-5x+7, form a quadratic polynomial whose zeroes are 3a and 3B.​

Answers

Answered by Anonymous
38

Correct Question

⇒If α, β are the zeroes of the polynomial 2x²+5x-7, form a quadratic polynomial whose zeroes are 3α and 3β .

Solution

Given Equation

⇒2x² +5x - 7 = 0

To Find

⇒α and β

⇒Form a Quadratic equation whose zeroes 3α + 3β

Now Take

⇒2x² +5x - 7 = 0

Use Middle term Splitting

⇒2x² +7x - 2x - 7 = 0

⇒x(2x +7) -1(2x + 7)= 0

⇒(x - 1) = 0 and 2x + 7 = 0

⇒x = 1 and 2x = -7

⇒x = 1 and x = -7/2

We get

⇒α = 1 and β = -7/2

Then

⇒3α = 3  and 3β = -21/2

General Equation

⇒x² - (sum of zeroes)x +  Product of zeroes = 0

Now we get

⇒x² - (3-21/2)x + 3×-21/2 = 0

⇒x² - {(6-21)/2}x - 63/2 = 0

⇒x² + (15/2)x - 63/2 = 0

Taking Lcm

⇒2x² + 15x - 63 = 0

Answer

⇒Equation is 2x² + 15x - 63 = 0

Answered by Anonymous
75

Answer:

Correct Question :-

  • If α , β are the zeroes of the polynomial 2x² + 5x - 7, form a quadratic polynomial whose are 3α , 3β.

Given :-

  • 2x² + 5x - 7

To Find :-

  • What is the quadratic polynomial whose zeroes are 3α and 3β.

Solution :-

Given equation :

2x² + 5x - 7 = 0

2x² + (7 - 2)x - 7 = 0

2x² + 7x - 2x - 7 = 0

x(2x + 7) - 1(2x + 7) = 0

(2x + 7)(x - 1) = 0

(2x + 7) = 0

2x + 7 = 0

2x = - 7

x = - 7/2

Either,

(x - 1) = 0

x - 1 = 0

x = 1

Hence, we get :

α = 1

β = - 7/2

Now, as we know that :

- (α + β)x + (αβ) = 0

Then,

3α = 3 × 1 = 3

3β = 3 × (- 7/2) = - 7 × 3/2 = - 21/2

Now, according to the question by using the formula we get,

x² - (3 - 21/2)x + (3 × {- 21/2} ) = 0

x² - (6 - 21/2)x + (- 63/2) = 0

x² - (- 15/2)x - 63/2 = 0

x² + (15/2)x - 63/2 = 0

2x² + 15x - 63/2 = 0

By doing cross multiplication we get,

2x² + 15x - 63 = 0 × 2

2x² + 15x - 63 = 0

The quadratic polynomial whose zeroes are and 3β is 2x² + 15x - 63 = 0.

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