Find the nature of roots for the given equations:
a) (x + 1) ( x+ 2) + x = 0
b) 4x2 – 12x – 9 = 0
class 1o ch-quadratic eqn
Answers
Step-by-step explanation:
1. Determine the nature of the roots of the following quadratic equations:
Important Notes:
– A quadratic equation is in the form ax2 +bx +c =0
– To find the nature of roots, first find determinant “D”
– D = b2 – 4ac
– If D > 0, equation has real and distinct roots
– If D < 0, equation has no real roots
– If D = 0, equation has 1 root
(i) 2x2 -3x + 5 =0
Solution:
Here, a= 2, b= -3, c= 5
D = b2 – 4ac
= (-3)2 -4(2)(5)
= 9 – 40
= -31<0
It’s seen that D<0 and hence, the given equation does not have any real roots.
(ii) 2x2 -6x + 3=0
Solution:
Here, a= 2, b= -6, c= 3
D = (-6)2 -4(2)(3)
= 36 – 24
= 12>0
It’s seen that D>0 and hence, the given equation have real and distinct roots.
(iii) (3/5)x2 – (2/3) + 1 = 0
Solution:
Here, a= 3/5, b= -2/3, c= 1
D = (-2/3)2 -4(3/5)(1)
= 4/9 – 12/5
= -88/45<0
It’s seen that D<0 and hence, the given equation does not have any real roots.
(iv) 3x2 – 4√3x + 4 = 0
Solution:
Here, a= 3, b= – 4√3, c= 4
D = (- 4√3)2 -4(3)(4)
= 48 – 48
= 0
It’s seen that D = 0 and hence, the given equation has only 1 real and equal root.