Question

If a and B are the zeroes of the polynomial 2x^2 - 13x + 6, then a + ß is
equal to​

Answer 1

$\displaystyle \sf{ \alpha + \beta = \frac{13}{2} }$

Correct question : If α and β are zeroes of the polynomial 2x² - 13x + 6 then α + β is equal to

Given :

α and β are zeroes of the polynomial 2x² - 13x + 6

To find :

The value of α + β

Concept :

If $\sf \alpha \: \: and \: \: \beta \:$are the zeroes of the quadratic equation $\sf{ a {x}^{2} + bx + c= 0}$

Then

$\displaystyle \sf \alpha + \beta \: = - \frac{b}{a} \: \: and \: \: \: \alpha \beta \: = \frac{c}{a}$

Solution :

Step 1 of 3 :

Write down the given polynomial

Here the given polynomial is 2x² - 13x + 6

Step 2 of 3 :

Write down the coefficients

Comparing the given polynomial with general quadratic polynomial ax² + bx + c we get

a = 2 , b = - 13 , c = 6

Step 3 of 3 :

Find the value of α + β

Here it is given that α and β are zeroes of the polynomial 2x² - 13x + 6

Then we have

$\displaystyle \sf{ \alpha + \beta = - \frac{b}{a} = - \frac{-13}{2} = \frac{13}{2} }$

$\displaystyle \sf{ \alpha \beta = \frac{c}{a} = \frac{6}{2}= 3 }$

Hence we can conclude that ,

$\boxed{ \: \: \displaystyle \sf{ \alpha + \beta = \frac{13}{2} \: \: }}$

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