Question

find value of k explain it

Answer 1

Hi,

firend.... this problem is simple....

just follow through my explaination....

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First of all we need to understand basic problem solving technique for quadratic equs....

suppose we are given with general quadratic quation

p(x) = $ax^{2} + bx + c$

where a , b and c are respective cooeficients of the powers of x;

and $\alpha and \beta$ are the roots of this equation....

then,

1) $\alpha + \beta = -\frac{b}{a}$

and

2) $\alpha \beta = \frac{c}{a}$

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now with this knowladge we proceed to solve the problem.....

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given

p(x) = $kx^{2} + 4x + 4$

and

$\alpha^2 + \beta^2 = 24$

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we use 1) and 2) to get results

1) $\alpha + \beta = -\frac{4}{k}$

and

2) $\alpha \beta = \frac{4}{k}$

and we use

$(\alpha + \beta)^{2} = \alpha^2 + \beta ^2 + 2\alpha \beta$

...

substituting...

we end up with

$\frac{16}{k^2} = 24 + 2(\frac{4}{k})$

=> $16 = 24k^2 + 8 k$

solving for k;

we get two values for k;

k= (-1 , 2/3)

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Ps. enjoy :)