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Maths Formula Pocket BOOK Maths Formula-Page1
Course: Mathematics in the Modern World (Math 11n)
50 Documents
Students shared 50 documents in this course
University: Visayas State University
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MATHS FORMULA - POCKET BOOK MATHS FORMULA - POCKET BOOK
E D U C A T I O N S
, 608-A, TALWANDI KOTA (RAJ.) Ph. 0744 - 6450883, 2405510
E D U C A T I O N S
, 608-A, TALWANDI KOTA (RAJ.) Ph. 0744 - 6450883, 2405510
QUADRATIC EQUATION & EXPRESSION
1. Quadratic expression :
A polynomial of degree two of the form ax2 + bx + c, a ≠ 0 is
called a quadratic expression in x.
2. Quadratic equation :
An equation ax2 + bx + c = 0, a ≠ 0, a, b, c ∈ R has two and
only two roots, given by
α = −+ −b b ac
a
24
2and β = −− −b b ac
a
24
2
3. Nature of roots :
Nature of the roots of the given equation depends upon the
nature of its discriminant D i.e. b2 4ac.
Suppose a, b, c ∈ R, a ≠ 0 then
(i) If D > 0 ⇒roots are real and distinct (unequal)
(ii) If D = 0 ⇒roots are real and equal (Coincident)
(iii) If D < 0 ⇒roots are imaginary and unequal i.e.
non real complex numbers.
Suppose a, b, c ∈ Q a ≠ 0 then
(i) If D > 0 and D is a perfect square ⇒ roots are rational
& unequal
(ii) If D > 0 and D is not a perfect square ⇒roots are
irrational and unequal.
For a quadratic equation their will exist exactly 2 roots real
or imaginary. If the equation ax2 + bx + c = 0 is satisfied for
more than 2 distinct values of x, then it will be an identity &
will be satisfied by all x. Also in this case a = b = c = 0.
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4. Conjugate roots :
Irrational roots and complex roots occur in conjugate pairs
i.e.
if one root α + iβ, then other root α iβ
if one root α + β, then other root α β
5. Sum of roots :
S = α + β = −b
a = −Coefficient of x
Coefficient of x2
Product of roots :
P = αβ = c
a = cons t term
Coefficient of x
tan
2
6. Formation of an equation with given roots :
x2 Sx + P = 0
⇒x2 (Sum of roots) x + Product of roots = 0
7. Roots under particular cases :
For the equation ax2 + bx + c = 0, a ≠ 0
(i) If b = 0 ⇒ roots are of equal magnitude but of opposite
sign.
(ii) If c = 0 ⇒ one root is zero and other is b/a
(iii) If b = c = 0 ⇒ both roots are zero
(iv) If a = c ⇒ roots are reciprocal to each other.
