Question

$find \: the \: value \: of \: k \: so \: that \: the \: zeroes \: of \: the \: quadratic \: polynomial \: 3x {}^{2} - kx + 14 \: are \: in \: the \: ratio \: \frac{7}{6}$
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Answer 1

Since the zeroes are in the ratio 7:6,

lemme assume that the zeroes are 7z and 6z

So...

➡️As u know sum of zeroes=-b/a =k/3= 7z+6z

So k/3=13z

so k=39z(eq1)

➡️Also product of zeroes=c/a= 14/3= 7z×6z= 42z²

So z²=1/9

So z=+or-1/3(eq2)

Substituting eq2 in eq1,

➡️If z=+1/3, then k=+13

➡️If z=-1/3, then k= -13

Hope it helped u ☺️

Notify me if there's any careless error