If the product of 2 roots of eqution is -31 then find the value of k
Solution
Product of 4 roots = -2015
product of 2 roots = -31
so product of other 2 roots = -2015/(-31) = 65
so 2 quadratic factors are x^2+ax-31 and x^2+bx +65 where a and b are to be determined
so x^4-18x^3+kx^2+174x - 2015=(x^2+ax-31)(x^2+bx +65)
or x^4 + (a+b)x^3 +(65-31+ab)x^2 + (65a - 31b)x - 2015=0
comparing coefficients we get
a+b= -18, (65a-31b= 174,k= 34 + ab
we can solve 1st 2 to get a= -4, b= -14 so putting in 3rd we get k= 34 + ab= 90
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