Quadratic Equations. Flashcards
Formula for when one root of a quadratic equation is k times the other root ?
(k+1)²/k= b²/ac
Solution of a quadratic eq by factorisation method
ax²+bx+c= a(x-α)(x-β)=0
Solution of a quadratic eq by direct method
α,β= -b±√b²−4ac/ 2a
What is the nature of root of quardratic eq when
D0
D= perfect square.
D0 implies real and distinct roots
D=0 implies real and equal roots
D= perfect square implies roots are unequal and rational.
Sum of roots and product of roots of a quadratic eq ?
α+β= -b/a αβ= c/a
Difference of roots of a quadratic eq?
α−β= ±√D/a
Sum of squares of roots of quadratic eq
α²+β²= b²−2ac/ a²
Difference of squares of roots of a quadratic eq
α²−β²= ±b√D/ a²
Sum of cube of roots of quadratic eq
α³+β³= -b(b²-3ac)/ a³
Difference of cube of roots of quadratic eq
α³−β³= ± (b²-ac) √D / a³
In quadratic eq, what is
α²+αβ+β² equal to ?
α²+αβ+β² = b²−4ac/ ac
In quadratic eq, what is α/β + β/α equal to
α/β + β/α = b² - 2ac/ ac
In quadratic eq what is α²β+β²α equal to ?
α²β+β²α=-bc/a
Form a quadratic eq from its given roots
x²-( α+β )x+ αβ= 0
Quadratic eq whose roots are k times the roots of q given quadratic eq
ax²+kbx+k²c=0
Quadratic eq whose roots are 1/k times the roots of a given quadratic eq
k²ax+kbx+c=0
Condition for one root common of a quadratic eq ?
(c1a2-c2a1)²=(b1c2-b2c1)(a1b2-a2b1)
Condition for two roots common of a quadratic eq
a1/a2 = b1/b2 = c1/c2
Condition for both rots of a quadratic eq to be greater than a number
D>=0
-b/2a>k
af(k)>0
Condition for both roots of a quadratic eq to be smaller than a number
D>=0
-b/2a0
Condition for both roots of a quadratic eq to be between 2 numbers
D>=0
k10
af(k2)>0
Condition for a number to lie between the roots of a quadratic eq
af(k)0
