Question

a) given the quadratic equation hx^2+kx+6=0 where h and k are constant.
i) if the equation has two equal roots, express h in terms of k.
ii) if h=6 and the quadratic equation has two different roots, find the range of values of k

b) given the straight line y=mx+3 does not intercept the curve y=2x^2 +x+5. find the range of values of m.

Answer 1

If it has 2 equal roots, then it means that discriminant=0.
If it has 2 distinct roots, then discriminant>0.

Answer 2

Want me to elaborate further? :)

Answer 3

@blockcolder yes sure.

Answer 4

\[\large \sqrt{k^2-24h}=0 \Rightarrow k^2=24h \Rightarrow h=\frac{k^2}{24}\\
\large \sqrt{k^2-24h}>0 \Rightarrow \sqrt{k^2- 144}>0 \Rightarrow k^2>144 \Rightarrow k<-12 \text{ or } k>12\].

Answer 5

Cant get it..huhu
how u get the 24 h?

Answer 6

\[\text{Discriminant }=\sqrt{b^2-4ac}\]
In this case, a=h, b=k, and c=6. :)

Answer 7

@Daenio @Callisto @Kreshnik @Mani_Jha CAN HELP ME, PLEASE?

Answer 8

Where are you stuck now? @gF

Answer 9

from the start...huhu

Answer 10

As blockcolder already said, equal roots mean that the value of b^2-4ac is 0. a,b, are the coefficients of x^2, x terms and c is the constant one. In the given equation, the coefficient of x^2 is h, of x is k, and the constant term is 6.
So a=h b=k and c =6
Now b^2-4ac=0
or, k^2-4*6*h=0
Now ok for the first part?

Answer 11

yes..then?

Answer 12

\[k ^{2}=24h\]
\[h=k ^{2}/24\]
For the next part, if the roots are different, b^2-4ac is not zero but is greater than zero(which means it is positive).
k^2-24h>0
Substitute the given value of h=6