Quadratic Equation Class 10 Notes | EduRev

 Page 1


•Intro:  We already know the standard 
form of a quadratic equation is:   
y = ax
2
 + bx + c 
•The constants are:  a , b, c 
•The variables are:  y, x 
Page 2


•Intro:  We already know the standard 
form of a quadratic equation is:   
y = ax
2
 + bx + c 
•The constants are:  a , b, c 
•The variables are:  y, x 
•The ROOTS (or 
solutions) of a 
polynomial are its 
x-intercepts 
•Recall:  The x-
intercepts occur 
where y = 0. 
Roots
Page 3


•Intro:  We already know the standard 
form of a quadratic equation is:   
y = ax
2
 + bx + c 
•The constants are:  a , b, c 
•The variables are:  y, x 
•The ROOTS (or 
solutions) of a 
polynomial are its 
x-intercepts 
•Recall:  The x-
intercepts occur 
where y = 0. 
Roots
•Example:  Find the 
roots: y = x
2
 + x - 6 
•Solution:  Factoring:  
y = (x + 3)(x - 2) 
•0 = (x + 3)(x - 2) 
•The roots are:   
•x = -3; x = 2 
Roots
Page 4


•Intro:  We already know the standard 
form of a quadratic equation is:   
y = ax
2
 + bx + c 
•The constants are:  a , b, c 
•The variables are:  y, x 
•The ROOTS (or 
solutions) of a 
polynomial are its 
x-intercepts 
•Recall:  The x-
intercepts occur 
where y = 0. 
Roots
•Example:  Find the 
roots: y = x
2
 + x - 6 
•Solution:  Factoring:  
y = (x + 3)(x - 2) 
•0 = (x + 3)(x - 2) 
•The roots are:   
•x = -3; x = 2 
Roots
•But what about 
NASTY trinomials 
that don’t factor? 
•Abu Ja'far Muhammad 
ibn Musa Al-Khwarizmi 
•Born: about 780 in 
Baghdad (Iraq) 
•Died: about 850 
Page 5


•Intro:  We already know the standard 
form of a quadratic equation is:   
y = ax
2
 + bx + c 
•The constants are:  a , b, c 
•The variables are:  y, x 
•The ROOTS (or 
solutions) of a 
polynomial are its 
x-intercepts 
•Recall:  The x-
intercepts occur 
where y = 0. 
Roots
•Example:  Find the 
roots: y = x
2
 + x - 6 
•Solution:  Factoring:  
y = (x + 3)(x - 2) 
•0 = (x + 3)(x - 2) 
•The roots are:   
•x = -3; x = 2 
Roots
•But what about 
NASTY trinomials 
that don’t factor? 
•Abu Ja'far Muhammad 
ibn Musa Al-Khwarizmi 
•Born: about 780 in 
Baghdad (Iraq) 
•Died: about 850 
•After centuries of 
work, 
mathematicians 
realized that as long 
as you know the 
coefficients, you can 
find the roots of the 
quadratic.  Even if it 
doesn’t factor! 
y ? ax
2
?bx ? c,  a ? 0
x ?
?b ? b
2
? 4ac
2a