Q.2 What is the nature of the roots of the quadratic equation 4² + 4√3 + 3 = 0.
Answers
We know that D = b^2 - 4 * a * c
= (4root3)^2 - 4 * 4 * 3
= 16 * 3 - 48
= 48 - 48
= 0
So, given quadratic equation has equal real roots.
Hope this helps!
Answer:
CORRECT QUESTION:
What is the nature of roots of quadratic equation 2x²+3x-4=0?
SOLUTION:
Nature of the roots of any quadratic equation can be find by applying formula of discriminant. Nature of roots can be expressed as follows:-
\begin{gathered}\qquad\qquad\quad\large{\sf{Nature\: of\: roots}}\\\\\boxed{\begin{array}{|c||c|}\cline{1-2}\bf{Discriminant}&\bf{Nature}\\\cline{1-2}\sf{+ve}&\sf{2\: distinct\:roots}\\\cline{1-2}\sf{-ve}&\sf{No\:real\:roots}\\\cline{1-2}\sf{0}&\sf{2\: equal\:roots}\cline{1-2}\cline{1-2}\end{array}}\end{gathered}
Natureofroots
\cline1−2Discriminant
\cline1−2+ve
\cline1−2−ve
\cline1−20
Nature
2distinctroots
Norealroots
2equalroots\cline1−2\cline1−2
\rule{250}{2}
In the given quadratic equation:-
a=coefficient of x²=2
b=coefficient of x=3
c=constant term=-4
\rule{250}{2}
We have formula of discriminant:-
\underline{\boxed{\sf{D=b^{2}-4ac}}}\star
D=b
2
−4ac
⋆
\sf{D=3^{2}-4(2)(-4)}D=3
2
−4(2)(−4)
\sf{D=9+32}D=9+32
\sf{D=41}D=41
Here the value of D is +ve, so:-
\Large{\underline{\boxed{\bf{NATURE}\longrightarrow\sf{2\: distinct\:roots}}}}
NATURE⟶2distinctroots