Question

If one root of a quadratic equations 8x²-Kx+3=0 is 1½, determine the value of K and hence the other root

Answer 1

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