If one root of a quadratic equations 8x²-Kx+3=0 is 1½, determine the value of K and hence the other root
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The polynomial is 9x²-18x+K
Let one root be y
Then the other root will be 2y
According to relation between coefficients and roots
Sum of roots= -(Coefficient of x)/Coefficient of x²
=> y+2y = -(-18)/9
=> 3y = 2
=> y = 2/3
So 2/3 is a root of the polynomial.
=> 9(2/3)² -18(2/3)+K = 0
=> 4–12+K=0
=> K = 8
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