Formulas Flashcards
a * b =
LCM(a. b) * HCF(a . b)
LCM of p³q and q4p
p³q4
if we have to find at what time two or three bells will ring at same time
find LCM
Quadratic equation form
ax²+bx+c=0
Cubic equation form
ax³+bx²+cx+d=0
How many zeros will quadratic and cubic equation will have respectively
2 and 3
If ax³+bx²+cx+d is completely divisible by ax²+bx+c that means
α and β of quadratic equation also will be the two zeros of cubic equation .
α+β=
-b/a
αβ=
c/a
Quadratic equation in the form of (α+β) & αβ
x² - (α+β)x + αβ = 0
α²+β²=
(α+β)² - 2αβ
α³+β³=
(α+β)³ - 3αβ(α+β)
1/α + 1/β =
(α+β)/αβ
If a curve cuts x-axis and y-axis. 3 times and 5 times respectively then equation ay²+by+c will have how many zeros
5
If a curve cuts x-axis and y-axis. 3 times and 5 times respectively then equation ax²+bx+c will have how many zeros
3
Condition for coincident lines
a1/a2 = b1/b2 = c1/c2 (infinitely many solutions)
Condition for intersecting lines
a1/a2 not equals to b1/b2(only one solution)
Condition for parallel lines
a1/a2 = b1/b2 not equals to c1/c2(no solutions)
Formula to find x of equation ax²+bx+c=0
x = (-b +- √D)/ 2a
Formula of discriminant
D = b²-4ac
If D = 0
equal roots
If D > 0
different roots
If D < 0
no real roots
an =
a +(n-1)d
Sn =
n/2 (2a + (n-1)d)
Formula of Sn with l
Sn = n/2 ( a + l )
Distance Formula =
√(x2-x1)² + (y2-y1)²
Section formula =
(mx2 + nx1)/ m+n
Similarity criteria for triangles
SSS.(ratio) SAS. AAA.
The tangent at any point of a circle is ——– to the radius through the point of contact
perpendicular
The lengths of tangents drawn from an external point to a circle are
equal.
Sin x
= P/H
cos x
= B/H
Tan x
= P/B
Sec x
= H/B
Cosec x
= H/P
Cot x
= B/P
