Question

$the \: zeroes \: of \: {x}^{2} - kx + 6 \: are \: in \: the \: ratio \:$
3:2,find k

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Answer 1

Let the zeros be 3x and 2x.

According to the equation

Product of roots =

constant term / coefficient of x^2.

= 6.

3x × 2x = 6.

x^2 = 1

Therefore x = 1 .

Now the roots are 3 and 2 .

Since

coefficient of x / coefficient of x^2 is the sum of roots in this case it is k.

k = 3 + 2 = 5

Answer 2

$<b>Hello Friend$


$\mathsf{\implies The \: zeroes \: of \: x^{2} \: - \: kx \: + \: 6 \: are \: in \: the \: ratio \: 3 : 2}$


$\mathsf{\implies Let \: the \: zeroes \: of \: be \: 3x \: and \: 2x}$


$\mathsf {\implies Product \: of \: zeroes = {\dfrac {c}{a}}}$


$\mathsf {\implies 3x × 2x = 6}$


$\mathsf{\implies 6x^{2} = 6}$


$\mathsf {\implies x^{2} = {\dfrac{6}{6}}}$


$\mathsf {\implies x^{2} = 1}$


$\mathsf {\implies x = - 1 \: or + 1}$


$\mathsf {\implies Sum \: of \: zeroes = {\dfrac {- b}{a}}}$


$\mathsf {\implies 3x \: + \: 2x = {\dfrac {- ( - k )}{1}}}$


$\mathsf {\implies 5x = k}$


$\mathsf {\implies 5 × 1 = k}$


$\mathsf {\implies k = 5}$


$\mathsf {\implies 5 × - 1 = k}$


$\mathsf {\implies k = - \: 5}$


$\mathsf {\implies k = - \: 5 , 5 }$


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