Final revision 1st sec. 2nd term alg.
The quadratic equation ax2 + bx + c = 0 b,c ∈R , a≠0 .
If L & M are the roots of the quadratic equ. So:F(L) = 0 , (x – L) is a factor of the equ.
F(M) = 0 , (x – M) is a factor of the equ.
The formula
The discriminate is
If The discriminate is –ve then the equation has no real roots.
If The discriminate is +ve then the equation has two fifferent roots.
If The discriminate is 0 then the equation has two equal roots.(one root )
If L & M are the roots of the quadratic equ. So:
The sum of the roots (L + M) =
The product of the roots (L M) =
The quadratic equation is x2 – (the sum of the roots) x + the product of the roots = 0
Or
(x – L)(x – M) = 0
1)If a = 1 then (L + M ) = -b , LM = c
2) if b = 0 , then L + M = 0 è L = -M
3) If a = c , then the equ. è ax2 + bx + a = 0
Then LM = 1 è L =
1) COMPLETE:
1) if x = 3 is a root of x2 – 8x + c = 0 , then c = …….
2) if (x – 2) is a factor of x2 – 5x + 6 , then f(2) = ……..
3) if f(x) = 2x2 + bx + 9 & f(-2) = 15 , b = …
4) if f(x) = 2x2 +7x – 15 , then f(x) = 0 when x = ……..
5) if 3x2 – 9 = 0 , then the sum of the two roots = ……… & their product = …………
6) if one of the roots of the equ, x2 + (k-5) x – 9 = 0 is the a. inverse of the other , then k = …
7) if the sum of the two roots of the equ. 2x2 – 3x + 5c = 0 equals their product , then c = …….
8) the quadratic equ. Whose two roots are 3 & 5 , is …………
9) the quadratic equ. Whose two roots are 2/3 & 3/2 , is …………
10 ) if x = 3 is a root of x2 – 8x + c = 0 , then the other root is …..
11) the product of the roots of the equ. 3x + 4 = 2x2 equals …………..
12) if one root of the equ. X2 + 5x + (k – 3) = 0 is the m.inverse of the other. Then k = ……….