Given that X1 and X2 are the two roots of the equation 9x & sup2; - (4k-7) x-6k & sup2; = 0 about X, is there a real number k such that the absolute value of X1 / x2 = 3 / 2? If there is, find out the value of K; if not, explain the reason | Math enthusiast | Mathematical art

Given that X1 and X2 are the two roots of the equation 9x & sup2; - (4k-7) x-6k & sup2; = 0 about X, is there a real number k such that the absolute value of X1 / x2 = 3 / 2? If there is, find out the value of K; if not, explain the reason

Weida theorem
x1+x2=(4k-7)/9
x1x2=-2k²/3
If k = 0
Then 9x & sup2; + 7x = 0
X1 = 0, X2 = - 7 / 9, not in accordance with | X1 / x2 | = 3 / 2
So x1x2

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