pls help
1.show that x^2+hx+k=o has two distinct roots fer al;l negative valuse of k
2. find the values of k for which the x axis is a tangent to the curve y=3x^2-8x+5-k.For each value of k,find the coordiantes ffor the point of tangency.
3.Find the range of values of k for whch the equation x^2 +5x+3=k has two real and distinct roots
qn 3. i noe how to do but answer differnt from answer key so nid clarification
thks in advacne
1. prove b^2-4ac is always positive for negative values of k
2. b^2-4ac=0 (basically real and repeated root case)
3. b^2-4ac>0 (More hints: bring the k to the left hand side, then compute b^2-4ac>0)
can gimme final answer fer qn 2 and 3 ma i want check cuz my answer different from answer key i dunno is answer key wrong or i wrng
and can show mi the steps fer qn1 too? i understand alr but i dunno how to present teh proof
Originally posted by gobez14:and can show mi the steps fer qn1 too? i understand alr but i dunno how to present teh proof
x^2+hx+k=0
discriminant = h^2 - 4(1)(k) = h^2 -4k
h^2 is greater or = 0
k is always -ve, thus -4k is always +ve
Therefore h^2 - 4k is always +ve, ie >0
Thus, since determinant is always >0, equation will always have 2 distinct roots
discriminant, not determinant.
BTW, ts. h^2 is always >= 0 regardless of whether h is positive or negative.
Q2) x-axis tangent to the curve => curve touches the line y=0 only 1 time
so 3x^2-8x+5-k = 0 at only 1 point => 1 root
discriminant = 0
64 - 4(3)(5-k) = 0
4+12k = 0
k = -1/3 => help me check... all done without using paper... so not confirmed
Find value of x: 2 methods
1st method:
3x^2-8x+16/3 = 0
9x^2-24x+16 = 0
(3x - 4)^2 = 0
x=4/3
and y = 0 (on x-axis mah)
coordinates: (4/3, 0)
2nd method:
obviously, for an x^2 curve, ie curve with smiling face, the minimum point will be the point at tangent with the x-axis.
so dy/dx = 6x-8
x = 4/3 (same answer)
Originally posted by FirePig:discriminant, not determinant.
BTW, ts. h^2 is always >= 0 regardless of whether h is positive or negative.
Ok changed... Thanks...
Q3)
x^2
+5x+3=k
x^2
+5x+3-k=0
discriminant = 25 - 4(1)(3-k) >0
13 + 4k >0
k > -3.25