Question

Find the nature of the roots of the quadratic equation 3x2-4x+3=0

Answer 1

$\underline{\textsf{Given:}}$

$\textsf{Quadratic equation is}$

$\mathsf{3x^2-4x+3=0}$

$\underline{\textsf{To find:}}$

$\textsf{Nature of roots of the given equation}$

$\underline{\textsf{Solution:}}$

$\underline{\mathsf{Concept\;used:}}$

$\mathsf{Discriminant\;of\;the\;quadratic\;equation\;ax^2+bx+c=0\;is\;\triangle=b^2-4ac}$

$\mathsf{Consider,}$

$\mathsf{3x^2-4x+3=0}$

$\mathsf{Here,a=3,b=-4,c=3}$

$\textsf{Now,}$

$\mathsf{\triangle=b^2-4ac}$

$\mathsf{\triangle=(-4)^2-4(3)(3)}$

$\mathsf{\triangle=16-36}$

$\mathsf{\triangle=-20}$

$\mathsf{Since\;\triangle\,<\,0,\;the\;roots\;are\;unreal}$

$\therefore\textsf{The given equattion has imaginary roots}$

$\underline{\textsf{Find more:}}$

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Answer 2

Answer:

3x²+4x+3=0

a=3,b=4,c=3

b²-4ac

(4)²-4(3)(3)

=16-36

-20