[tex]\leadsto[/tex] The general form of equation is ax²+bx +c.
[If a =0then the equation becomes to a linear equation. If b =0then the roots of the quadratic equation becomes equal but opposite in sign. If c =0then one of the roots is zero. ]
[tex]\leadsto[/tex] b²=4acis thediscriminateof theequation. There aretworoots.
i)When b² – 4ac = 0, then roots are real & equal.
ii) When b² – 4ac > 0, then the roots are imaginary and unequal.
iii)When b² – 4ac < 0, then there will be no roots.
Answer:
Given :-
To Find :-
Solution :-
[tex] \longmapsto \sf {x}^{2} + 4x + 1 =\: 0[/tex]
By comparing the quadratic equation x² + 4x + 1 = 0 with the quadratic equation ax² + bx + c = 0 [ a ≠ 0] , we get :
Now,
[tex]\mapsto[/tex] The discriminate = 0
Then, b² – 4ac = 0
↦ [tex]\sf Discriminate =\: {(4)}^{2} – 4 \times 1 \times 1[/tex]
↦ [tex]\sf Discriminate =\: 4 \times 4 – 4[/tex]
↦ [tex]\sf Discriminate =\: 16 – 4[/tex]
➲ [tex]\sf\bold{\red{Discriminate =\: 12}}[/tex]
[tex]\therefore[/tex] The discriminate of the quadratic equation x² + 4x + 1 = 0 is 12 .
Hence, the correct options is option no (a) 12.
[tex]\rule{300}{2}[/tex]
Extra Information :–
[tex]\leadsto[/tex] The general form of equation is ax² + bx + c.
[ If a = 0 then the equation becomes to a linear equation. If b = 0 then the roots of the quadratic equation becomes equal but opposite in sign. If c = 0 then one of the roots is zero. ]
[tex]\leadsto[/tex] b² = 4ac is the discriminate of the equation. There are two roots.
i) When b² – 4ac = 0, then roots are real & equal.
ii) When b² – 4ac > 0, then the roots are imaginary and unequal.
iii) When b² – 4ac < 0, then there will be no roots.
Given Equation
x² + 4x + 1 = 0
To Find
Discriminant
So Compare with
ax² + bx + c = 0
We get
a = 1 , b = 4 and c = 1
Formula
D = b² – 4ac
Now
D = (4)² – 4 × 1 × 1
D = 16 – 4
D = 12
Answer
D = 12 , Option (a) is correct
More Information
When D > 0
It is real and Distinct
When D = 0
It is equal and real roots
When D<0
No real roots