Question

pls solve it ...

4) Find K, if the sum of the roots of the quadratic equation
4x2 + 8kx + k +9= 0 is equal to their product.​

Answer 1

Hi !

Solution :-

Given equation , 4x² + 8kx + k + 9 = 0

As we know that ,

$( \alpha + \beta ) = \frac{ - b}{c}$

since,

$( \alpha + \beta ) = \frac{ - 8k}{4} = - 2k$

And ,

$( \alpha \beta ) = \frac{k + 9}{4}$

according to question ,sum of roots = product of roots since,

-2k = k + 9/4

-8k = k + 9

-9k = 9

k= - 1 Answer !

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Hope it helps you !!

@Rajukumar111

Answer 2

Given,

$4 {x}^{2} + 8kx + k + 9 = 0$

a=4, b=8k and c=k+9

As we know

$\alpha + \beta = \frac{ - b}{a} = \frac{ - 8k}{4} = - 2k\\ and \\ \alpha \beta = \frac{c}{a} = \frac{k + 9}{4}$

A/c to question

sum of roots =product of roots

$= > - 2k = \frac{k + 9}{4} \\ = > - 8k = k + 9 \\ = > - 9k = 9 \\ = > k = \frac{ - 9}{9} \\ = > k = - 1$