O-Level Additional Mathematics. Helps needed!

Find the values of k for which the quadratic equation 9x^2 - kx + (k-7) =0 has one positive and one negative root.

Find the values of k for which the quadratic equation 9x^2 - kx + (k-7) =0 has one positive and one negative root.

Let the 2 roots be

x_1

and

x_2

then the equation

9(x-x_1)(x-x_2)=0

from this the original equation is

9x^2-9(x_1+x_2)x+9x_1x_2=0

so for k

9x_1x_2=k-7<0

because one of the root is positive the other is negative
Another limit for k is that there should be two real roots
that is

k^2-36(k-7)>0

but for k-7<0 this equation is always true.
From this follows ...... ???

(edited 11 years ago)

agree with ztibor

in general the product of roots is c/a which in this case is ( k-7 )/9 and this must be negative

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