Math, asked by kash2404, 10 months ago

2.V
02
Solve the following: (any 1)
Ifa + B = 8 and a +ß? = 34, find the quadratic equation whose roots are a, and B.


Answers

Answered by Aloi99
34

Answer:

QUESTION:-

if \:  \alpha  +  \beta  = 8 \:  \\  \alpha  \beta  = 34 \\ find \: qudratic \: equation

Step-by-step explanation:

SOLUTION:-

we \: know \:  \alpha  +  \beta  = 8 \: and \:  \alpha  \beta  = 34

Using quadratic Formula↓

k( {x}^{2}   - ( \alpha  +  \beta )x +  \alpha  \beta )

Inserting the Values we get↓

k( {x}^{2} - 8x + 34)

Let K=1

WE GET=>-8x+34 as the quadratic EQUATION✓

The quadratic equation can be expressed in the form↓

[-(Sum of Roots)+Product of Roots]=0

Hope IT Helps

 \mathcal{BE \: BRAINLY}

Answered by Anonymous
51

\huge{\underline{\underline{\red{\mathfrak{AnSwEr :}}}}}

{\underline{\sf{\blue{Given :}}}}

  • α + β = 8

  • αβ = 34

\rule{200}{1}

{\underline{\sf{\green{Solution :}}}}

We have formula for equation :

\star {\boxed{\sf{k \bigg( x^2 \: - \: ( Sum \: of \: zeros)x \: + \: Product \bigg) }}}

Here zeroes are α and β

\implies {\sf{k \bigg( x^2 \: - \: (\alpha \: + \: \beta)x \: + \: \alpha \beta \bigg) }}

Substitute values of α and β

\implies {\sf{k \bigg( x^2 \: - \: (8)x \: + \: 34 \bigg) }}

Where k = 1

So,

\implies {\sf{x^2 \: - \: 8x \: + \: 34}}

Quadratic Polynomial is - 8x + 34

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