Question

if alpha and beta are the zeros of quadratic polynomial f(x) = x² - 5x+k and Alpha minus beta is equal to 1 find the value of k

Answer 1

Given equation :

x² - 5x + k

On comparing with ax² + bx + c, we get

a = 1, b = - 5 and c = k

Now,

$\alpha + \beta$ = - b / a

= - ( - 5 ) / 1

= 5

It is given that

$\alpha - \beta$ = 1 ____( 1 )

•°•

Add these two

$\alpha + \beta + \alpha - \beta$ = 5 + 1

2 $\alpha$ = 6

$\alpha$ = 3

Now,

Put this value in ( 1 ), we get

3 - $\beta$ = 1

$\beta$ = 2

As we know that,

$\alpha \beta$ = c / a

Putting values, we get

3 × 2 = k / 1

k = 6

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