Quadratic Equations.

Question 1

Formula for when one root of a quadratic equation is k times the other root ?

Answer 1

(k+1)²/k= b²/ac

Question 2

Solution of a quadratic eq by factorisation method

Answer 2

ax²+bx+c= a(x-α)(x-β)=0

Question 3

Solution of a quadratic eq by direct method

Answer 3

α,β= -b±√b²−4ac/ 2a

Question 4

What is the nature of root of quardratic eq when
D0
D= perfect square.

Answer 4

D0 implies real and distinct roots
D=0 implies real and equal roots
D= perfect square implies roots are unequal and rational.

Question 5

Sum of roots and product of roots of a quadratic eq ?

Answer 5

α+β= -b/a 
αβ= c/a

Question 6

Difference of roots of a quadratic eq?

Answer 6

α−β= ±√D/a

Question 7

Sum of squares of roots of quadratic eq

Answer 7

α²+β²= b²−2ac/ a²

Question 8

Difference of squares of roots of a quadratic eq

Answer 8

α²−β²= ±b√D/ a²

Question 9

Sum of cube of roots of quadratic eq

Answer 9

α³+β³= -b(b²-3ac)/ a³

Question 10

Difference of cube of roots of quadratic eq

Answer 10

α³−β³= ± (b²-ac) √D / a³

Question 11

In quadratic eq, what is

α²+αβ+β² equal to ?

Answer 11

α²+αβ+β² = b²−4ac/ ac

Question 12

In quadratic eq, what is α/β + β/α equal to

Answer 12

α/β + β/α = b² - 2ac/ ac

Question 13

In quadratic eq what is α²β+β²α equal to ?

Answer 13

α²β+β²α=-bc/a

Question 14

Form a quadratic eq from its given roots

Answer 14

x²-( α+β )x+ αβ= 0

Question 15

Quadratic eq whose roots are k times the roots of q given quadratic eq

Answer 15

ax²+kbx+k²c=0

Question 16

Quadratic eq whose roots are 1/k times the roots of a given quadratic eq

Answer 16

k²ax+kbx+c=0

Question 17

Condition for one root common of a quadratic eq ?

Answer 17

(c1a2-c2a1)²=(b1c2-b2c1)(a1b2-a2b1)

Question 18

Condition for two roots common of a quadratic eq

Answer 18

a1/a2 = b1/b2 = c1/c2

Question 19

Condition for both rots of a quadratic eq to be greater than a number

Answer 19

D>=0
-b/2a>k
af(k)>0

Question 20

Condition for both roots of a quadratic eq to be smaller than a number

Answer 20

D>=0

-b/2a0

Question 21

Condition for both roots of a quadratic eq to be between 2 numbers

Answer 21

D>=0
k10
af(k2)>0

Question 22

Condition for a number to lie between the roots of a quadratic eq

Answer 22

af(k)0